ADAPTIVELY FILTERING TRANS-IMPEDANCE AMPLIFIER FOR RF … · 2016-06-21 · ii Abstract Adaptively...

ADAPTIVELY FILTERING TRANS-IMPEDANCE AMPLIFIER FOR

RF CURRENT PASSIVE MIXERS

by

Tian Ya Liu

A thesis submitted in conformity with the requirements

for the degree of Master of Applied Science

Graduate Department of Electrical and Computer Engineering

University of Toronto

© Copyright 2016 by Tian Ya Liu

ii

Abstract

Adaptively Filtering Trans-Impedance Amplifier for RF Current Passive Mixers

Tian Ya Liu

Master of Applied Science

Graduate Department of Electrical and Computer Engineering

University of Toronto

2016

Current Passive Mixers represent the state of the art for the signal down-conversion in wireless

receivers. In such kind of structures, noise, distortion, and losses are strictly correlated to the

stage following the mixer. This thesis proposed a trans-impedance amplifier (TIA) to sense the

down-converted current with a new topology that adaptively filters the out-of-band interferers as

a function of input current magnitude with a class-AB transconductor in the feedback network.

The prototype is implemented in IBM 0.13μm CMOS technology, and shows low input

impedance with a high-pass shaped noise and distortion profile. The filter cut-off frequency is

reconfigurable between 2.8MHz and 12MHz. The prototype consumes 1.92mW of power from a

1.2V supply and the active die area is 0.45mm2. It achieves out-of-band SFDR between 86.8dB

and 75.1dB, with the FOM varies between 182 dB(J-1

) and 176 dB(J-1

).

iii

Acknowledgments

First and foremost, I would like to thank my supervisor Professor Antonio Liscidini for providing

me with detailed guidance and support. I am glad to be his first M.A.Sc student at University of

Toronto. His technical advices have been invaluable and memorable during the past two years. I

would also like to thank the committee members, Professor Liscidini, Professor Genov, Professor

Sheikholeslami and Professor Prodic for their time, valuable feedbacks, and comments.

Second, I would like to thank Jason (Chuanwei) Li for providing help with all the CAD tools and

layout techniques during my second year, and all the discussions we had. I would also like to

thank all the colleagues in BA5000 for all the interesting conversations and interactions we had.

Finally, I would like to thank my parents for all the support and understandings through the

duration of my master study and my life.

iv

Table of Contents

Acknowledgments ........................................................................................................................ iii

List of Tables ............................................................................................................................... vii

List of Figures ............................................................................................................................. viii

List of Acronyms .......................................................................................................................... xi

Chapter 1 ....................................................................................................................................... 1

Introduction ................................................................................................................................... 1

1.1 Motivation .......................................................................................................................... 1

1.2 Objective ............................................................................................................................ 2

1.3 Thesis Outline .................................................................................................................... 2

Chapter 2 ....................................................................................................................................... 3

Trans-Impedance Amplifier Overview ....................................................................................... 3

2.1 RF Receiver Basics and Specifications ............................................................................ 3

2.2 State-of-the-Art TIA Structure Overview ...................................................................... 4

2.3 TIA Input Impedance and Comparison ......................................................................... 9

2.4 TIA Noise and Comparison ............................................................................................ 13

2.5 Summary .......................................................................................................................... 19

Chapter 3 ..................................................................................................................................... 21

Proposed Trans-Impedance Amplifier ..................................................................................... 21

3.1 Structure and Transfer Function .................................................................................. 21

3.1.1 Finite Trans-Conductance and Gain Bandwidth Product .............................. 25

3.1.2 Reconfigurable TIA Filter .................................................................................. 30

3.2 Input Impedance ............................................................................................................. 34

3.3 Spurious-Free Dynamic Range ...................................................................................... 37

v

3.3.1 Noise Transfer Functions and Analysis ............................................................ 37

3.3.2 Linearity and Intermodulation Phenomena ..................................................... 41

3.4 Stability Analysis ............................................................................................................. 42

3.5 Adaptive Filtering Response .......................................................................................... 44

3.6 Summary .......................................................................................................................... 45

Chapter 4 ..................................................................................................................................... 46

System and Circuit Design ......................................................................................................... 46

4.1 Operational Amplifier in Feed-Forward Path ............................................................. 46

4.2 Operational Trans-conductance Amplifier in Feedback Network ............................. 50

4.3 Reconfigurable TIA with MOS switches and Capacitor banks .................................. 54

4.4 Stability Analysis ............................................................................................................. 55

4.5 Simulation Results .......................................................................................................... 59

4.6 Summary .......................................................................................................................... 64

Chapter 5 ..................................................................................................................................... 65

Measurement Results .................................................................................................................. 65

5.1 Test Setup ........................................................................................................................ 65

5.1.1 Device Under Test ............................................................................................... 65

5.1.2 Printed Circuit Board ......................................................................................... 66

5.1.3 Equipment Setup ................................................................................................. 68

5.2 TIA Measurement Results and Comparison ................................................................ 68

5.2.1 Filter Transfer Function ..................................................................................... 68

5.2.2 Input Impedance ................................................................................................. 70

5.2.3 Two-Tone Intermodulation Test ....................................................................... 71

5.2.4 Noise Measurement ............................................................................................. 74

5.2.5 Performance Summary and Comparison ......................................................... 75

Chapter 6 ..................................................................................................................................... 78

vi

Conclusion ................................................................................................................................... 78

6.1 Summary .......................................................................................................................... 78

6.2 Future Work .................................................................................................................... 78

Bibliography ................................................................................................................................ 80

vii

List of Tables

2.1 Design Specifications and Circuit parameters for Tow-Thomas Filter ..............................9

2.2 Design Specifications and Circuit parameters for Rauch Filter.........................................11

2.3 Summary of State-of-the-Art TIA Topologies and Comparison………………………...19

3.1 Design Specifications and Circuit parameters for the Reconfigurable TIA......................31

4.1 Summarized Stability Simulation Results.........................................................................55

4.2 Summary of Simulation Results .......................................................................................60

5.1 Summary of Measurement Results ...................................................................................72

5.2 Comparison with other published works ..........................................................................73

viii

List of Figures

2.1 The Zero-IF Receiver Architecture...........................................................................................3

2.2 WCDMA Out-of-band Blocker Test.........................................................................................4

2.3 State-of-the-Art Filtering TIA topologie...................................................................................4

2.4 Filtering TIA: Single Pole Virtual Ground with Large Grounded Capacitance ......................5

2.5 Filtering TIA: Two Real Poles with Switchable Compensation...............................................6

2.6 Filtering TIA: Tow-Thomas Biquad Filter ..............................................................................7

2.7 Filtering TIA: Current Driven Rauch Biquad Filter ................................................................8

2.8 Bode Plot - Input Impedance of Tow-Thomas Filter with varying GBP................................11

2.9 Bode Plot-Input Impedance of Rauch Filter with varying GBP…………………..............12

2.10 Tow-Thomas Filter with Noise Sources.................................................................................14

2.11 Tow-Thomas Filter Output Noise Transfer Function with Each Noise Source .....................16

2.12 Rauch Filter with Noise Sources ............................................................................................17

2.13 Rauch Filter Output Noise Transfer Function with Each Noise Source.................................19

3.1 Proposed Filtering TIA with zeros in the feedback network..................................................21

3.2 Original Filtering TIA with active feedback network.............................................................22

3.3 Bode plot - Transfer function of TIA current and Interferer current over Input current........24

3.4 Quality Factor as a Function of varying Trans-Conductance gm...........................................26

3.5 Bode plot –Transfer Function and Phase Response of the TIA with Increasing Trans-

Conductance gm......................................................................................................................27

3.6 Bode plot –Transfer Function and Phase Response of TIA With Real Parameters................29

3.7 Proposed Filtering TIA with Reconfigurable Cut-off Frequency ..........................................30

3.8 Bode Plot –Transfer Function of Amplitude and Phase Response with Re-configurable Cut-

off Frequency......................................................................................................................... 32

3.9 Bode Plot – Input Impedance Transfer Function of Proposed TIA Filter with Varying

Parameters...............................................................................................................................34

ix

3.10 Bode Plot – Input Impedance of Proposed TIA Filter with Reconfiguring Bandwidth and

Scaling Options.......................................................................................................................36

3.11 Proposed TIA Filter with Noise Sources................................................................................37

3.12 Proposed TIA Filter Output Noise Transfer Function with All Noise Source........................39

3.13 Proposed TIA Filter Intermodulation Product Phenomena.....................................................41

3.14 TIA Loop Gain Analysis – All Breaking Points.....................................................................42

3.15 TIA Loop Gain Analysis – Overall Loop Gain Bode Plot......................................................43

3.16 Bode Plot – Adaptive Transfer Function Sketch of Proposed TIA with Increasing Interferer

Power (Theoretical) ................................................................................................................44

4.1 Conventional TIA...................................................................................................................46

4.2 Small Signal Model of the Two-Stage Miller Compensated Op-Amp...................................47

4.3 Two-Stage Miller Compensated Op-Amp for the Proposed TIA...........................................48

4.4 Common Mode Feedback Amplifier for Two-Stage OP-AMP..............................................49

4.5 Simplified Scheme for CMOS Trans-conductor.....................................................................50

4.6 Proposed Operational Trans-conductance Amplifier with Bias in Class-A or Class-AB......51

4.7 OTA Output Voltages and Drain Currents with Different Input Current at 50MHz..............52

4.8 Common Mode Feedback Amplifiers for OTA......................................................................53

4.9 Reconfigurable TIA with Switch and Capacitor Banks..........................................................54

4.10 Reconfigurable TIA Top Level Schematic.............................................................................55

4.11 Bode Plot – Loop Gain of the TIA Main Loop.......................................................................56

4.12 Bode Plot – Loop Gain of the Feed-forward Op-Amp...........................................................57

4.13 Bode Plot – Loop Gain of the Op-Amp Common Mode Feedback........................................58

4.14 Bode Plot – Loop Gain of the OTA Common Mode Feedback..............................................58

4.15 Bode Plot - Simulated Reconfigurable TIA Signal Transfer Functions.................................59

4.16 Bode Plot - Simulated TIA Adaptive Transfer Function with Different Input Signal (cut-off

frequency at 3.1MHz) ............................................................................................................59

4.17 Bode Plot- Simulated Reconfigurable TIA Input Impedance Transfer Functions..................60

x

4.18 Simulated Output Noise – Comparison with State-of-the-Art Designs ([email protected]).......60

4.19 Simulated Output Noise – Reconfigurable TIA with High-pass Noise Shaping....................61

4.20 Two Tone Out-of-Band Linearity Test @10MHz and 19.5MHz for Lowest Band

Configuration..........................................................................................................................61

4.21 Two Tone Out-of-Band Linearity Test @50MHz and 95MHz for Highest Band

Configuration..........................................................................................................................62

5.1 Chip Die Photo........................................................................................................................66

5.2 Printed Circuit Board Block Diagram.....................................................................................67

5.3 Printed Circuit Boards.............................................................................................................68

5.4 Graphic User Interface for Measurement with LABVIEW....................................................68

5.5 Measured Transfer Function of the Reconfigurable TIA.......................................................69

5.6 Measured Adaptive Transfer Function of the TIA (Lowest Bandwidth) ...............................70

5.7 Measured Input Impedance of the Reconfigurable TIA.........................................................70

5.8 Measured Adaptive Input Impedance in Ohms (Lowest Bandwidth) ....................................71

5.9 Two Tone Tests: Output IM3 In-band High-pass Shaping (Lowest bandwidth) ...................72

5.10 IM3 Product Bends for Large Input Signal.............................................................................73

5.11 1-dB Compressing Point with Large Out-of-Band Input Signal............................................73

5.12 Measured Output Noise Spectrum for Lowest Bandwidth.....................................................74

5.13 Measured Output Noise Spectrum for Highest Bandwidth....................................................75

xi

List of Acronyms

CAD Computer Aided Design

CMOS Complementary metal–oxide–semiconductor

DR Dynamic Range

DUT Device Under Test

FOM Figure of Merit

FPGA Field-Programmable Gate Array

GBP Gain Bandwidth Product

GUI Graphical User Interface

IIP3 Third Order Input Intercept Point

IM Intermodulation

LNA Low Noise Amplifier

LTE Long-Term Evolution

NMOS N-Channel MOSFET

OP-AMP Operational Amplifier

OTA Operational Trans-conductance Amplifier

PCB Printed Circuit Board

PMOS P-Channel MOSFET

PVT Process Voltage Temperature

xii

Q Factor Quality Factor

RF Radio Frequency

SFDR Spurious-Free Dynamic Range

SMA SubMiniature version A

TIA Trans-Impedance Amplifier

USB Universal Serial Bus

WCDMA Wideband Code Division Multiple Access

CHAPTER 1. INTRODUCTION 1

Chapter 1

Introduction

1.1 Motivation

Nowadays, current passive mixers represent the state of the art for the signal down-conversion in

wireless receivers. In such kind of structures, noise, distortion and losses are strictly correlated to

the stage following the mixer. The most common solution adopted to sense the down-converted

current is a trans-impedance amplifier (TIA) in shunt with a ground capacitance that assures low

input impedance when the loop-gain of the amplifier decreases. Low input impedance is

necessary to have a small voltage swing at the output of the mixer (typically a few hundred mV)

to minimize the modulation of the switch resistance and with it the distortion produced during

the down-conversion. For the TIA to handle a small signal and a large out-of-band interferer, the

spurious-free dynamic range (SFDR) requirement becomes very challenging. A ground input

capacitance can be also used to filter the majority of the out-of-band interferers by transforming

the TIA into a filter [1],[2]. This reduces the dynamic range required by the TIA and its power

consumption. However, this advantage is often paid in terms of area and power since the limited

voltage swing tolerable at the input of the TIA demands a large capacitor to absorb the down-

converted interferers and higher power consumption in the amplifier to achieve a better linearity.

The idea originally proposed in [3] places an active feedback network only to improve out-of-

band large-signal attenuation and 1dB compression point. A TIA filter typically occupies 20%-

30% of the analog frond end in the receivers. This TIA in [3] consumes high power and uses a

large amount of capacitances (area) only for tolerating large input signals while keeping the input

voltage swing small. The idea in [3] is re-used in this thesis to target the implementation of a

TIA filter that breaks off these trade-offs and occupies small area with lower total capacitance;

provides low input impedance, and high SFDR with lower power consumption; utilizes the

characteristics of the structure to achieve an adaptive filtering response as a function of out-of-

band input current magnitude; and finally be able to reconfigure the filter cut-off frequency to

work between WCDMA standard and LTE standard.

CHAPTER 1. INTRODUCTION 2

1.2 Objective

The main objectives of this thesis are as follows:

1. Provide a background of existing TIAs for wireless applications and review their

architectures in terms of transfer functions, input impedance, noise and linearity.

2. Propose a low power TIA with small area that provides low input impedance, adaptive

filtering profile, high SFDR and Figure of Merit (FOM) among all the other existing designs.

3. Show theoretical equations, circuit-level simulations, implementations, and prototype

measurement results to validate the design.

1.3 Thesis Outline

Chapter 2. Trans-Impedance Amplifier Overview: This chapter describes the existing

solutions of TIAs and compares with the same specifications as the proposed design in terms of

transfer function, input impedance, noise and linearity.

Chapter 3. Proposed Trans-Impedance Amplifier: A new TIA topology is introduced by the

proposed design and the key properties of the filter are studied in detail, including transfer

functions, input impedance, Spurious-Free Dynamic Range, and re-configurability. The design

parameters and sizes of the capacitor and resistors are summarized at the end of the chapter.

Chapter 4. System and Circuit Design: This chapter describes each individual elements of the

TIA filter; Transistor level design choices are explained in detail. The simulation results are also

shown to verify the design including transfer function, input impedance, linearity, noise, power,

and re-configurability.

Chapter 5. Measurement Results: This chapter shows the measurement results of the TIA

prototype described in Chapter 4. The results are presented in graphs and tables to compare with

other state-of-the-art designs.

Chapter 6. Conclusion: This chapter summarizes the thesis and future work is discussed.

CHAPTER 2. TRANS-IMPEDANCE AMPLIFIEROVERVIEW 3

Chapter 2

Trans-Impedance Amplifier Overview

2.1 RF Receiver Basics and Specifications

Figure 2.1 shows the common architecture of the zero-IF receivers. In this architecture, RF

signal is directly translated to baseband, which is done by making the local osillator (LO)

frequency equal to the RF signal. Current passive mixer is often used for signal down-conversion

followed by a low-pass filtering trans-impedance amplifier in baseband.

The channel bandwidth is folded in half when it is converted down to baseband. The standard 3G

Wideband Code Division Multiple Access (WCDMA) channel length is 3.84MHz in the RF

receiver requirements [4], that makes 1.92MHz for the baseband section which contains the low-

pass filter and defines the minimum filter bandwidth. For 4G Long-Term Evolution (LTE), the

most common channel bandwidths are 5MHz, 10MHz, and 20MHz, which makes a maximum of

10MHz for the baseband filter.

Figure 2.2 shows the blocker test for the WCDMA baseband section. The maximum out-of-band

input referred power in the figure is -15dBm at 85MHz offset. Considering a total

transconductance of 40mS for typical LNA and mixer down-conversion [2], the maximum input

current amplitude for the baseband filter is approximately 2.24mA (a few mA).

Figure 2.1: The Zero-IF receiver architecture


2.2 State-of-the-Art TIA Structure Overview

Filtering TIA topologies shown in Figure 2.3 a-d) are the most common structures following the

current passive mixer in wireless receivers. Their transfer functions are studied in this section. At

DC, the in-band trans-impedance gain is set by the feedback resistance.

Figure 2.2: WCDMA Out-of-band blocker test

Figure 2.3: State-of-the-Art Filtering TIA topologies


In Figure 2.4, a large shunt capacitance Cs is used between the virtual ground of the Op-amp and

ground to filter out the far away interferers when the loop gain of the amplifier decreases. It is a

conventional low pass filter consist of a single pole introduced by R1C1, so the attenuation in the

filter stop-band is less compared to the filtering TIAs in Figure 2.3 b) - d).

The transfer function of this structure is:

(2.1)

As shown in the equation (2.1), the shunt capacitor Cs is not taken into account because the

amplifier is ideal and has an infinite gain bandwidth product. In fact, there will be more poles

introduced when finite gain bandwidth product (GBP) ωt of the amplifier is considered and it is

modeled by an integrator ωt/s. Now the transfer function simplifies to:

(2.2)

This structure is mainly limited by the number of poles and the GBP of the amplifier in terms of

selectivity (stop-band attenuation).

RF VOUT

Cs CsC1

R1

C1

R1

IINMixer

Figure 2.4: Filtering TIA - Single Pole Virtual Ground with Large Grounded Capacitance


The circuit used in [1] shown in Figure 2.5, the input current is fed to a CR filter followed by an

integrator as in Figure 2.4. An additional real pole is created by R2Cs and they can also be used to

control the feedback factor of the amplifier. This type of filter is usually referred as a biquad low

pass filter.

Biquad low pass filter has the following transfer function:

(2.3)


(2.4)

{

√

√

(2.5)

RF VOUT

Cs CsC1

R1

C1

R1

IINMixer R2

R2

Figure 2.5: Filtering TIA – Two Real Poles with Switchable Compensation


From equation (2.4), it is clear that the filter has two real poles, one at R1C1 and one at R2CS. The

average filter cut-off frequency can be estimated by equation (2.5). For real pole systems, the

quality factor Q in equation (2.5) is always less or equal to 0.5 [5], resulting in a poor selectivity

both out-of-band and in-band, depending on the two poles location. However, there will be no

peaking in the bode plot or overshoot in time-domain step response which tends to be more

stable.

In Figure 2.6, a well-known filter topology is shown which is called Tow-Thomas Biquad Filter.


(2.6)

{

√

√

(2.7)

RF

C1

R3

C1

R3

IINMixer

R1

OP1 OP2 VOUT

R2

C2

R1

C2

R2

Figure 2.6: Filtering TIA - Tow-Thomas Biquad Filter


With this topology, the filter cut-off frequency is the same as the previous one, but the two poles

can be complex-valued and conjugate pairs, ωp1 = ωp2* in this case, (i.e. Q > 0.5) and it is

governed by the ratio of the RC elements in equation (2.7). This topology is often used due its

ease of design. The gain can be controlled by varying a single resistance R1 and the Q factor can

be adjusted by varying a single resistance R3. The distortion (e.g. third order intermodulation

product IM3) is large when the input signals increase. In this kind of feedback structure, the

largest signal is defined by the feedback factor that is related to R1 which is usually large, so the

overall loop gain of this structure is also large due to the open-loop gain of the op-amps. Since

the feedback is connected to the second op-amp, it requires an even higher open-loop gain and

bandwidth of the op-amp resulting in high power consumption in order to reduce the nonlinearity.

In Figure 2.7, another popular filtering TIA is presented used in [2] called current driven Rauch

Biquad filter.


(2.8)

RF VOUT

Cs CsC1

R1

C1

R1

IIN

Mixer R2

R2

Figure 2.7: Filtering TIA – Current Driven Rauch Biquad Filter


{

√

√

(2.9)

As expected, the transfer function in equation (2.8) is also a biquad with the cut-off frequency set

by the two time constants R1Cs and R2C1. The reason it is used in [2] is because it can be easily

tuned(i.e. gain re-configurability) to improve the handling capability of different high-level out-

of-band interferers (more robust to fading) and while the current going into the virtual ground

through R2 will have a low input impedance to better meet the requirement at the output of the

mixer. The noise of this structure can also be reduced by decreasing the grounded capacitance C1,

with a cost of higher input impedance [2]. The linearity of the structure can be improved by

increasing the open-loop gain of the op-amp. The higher the open-loop gain is, the smaller the

voltage swing at the virtual ground node is which results in a higher linearity with a given output

swing. However, these advantages come at a cost of area which means a large capacitor to

ground (Cs) is required as in Figure 2.4 and Figure 2.5 to handle the large interferers to minimize

the swing at the input of the TIA.

2.3 TIA Input Impedance and Comparison

For all the filters introduced in the previous section, every TIA filter topology has its own

advantages and disadvantages, this section will focus on the analysis of input impedance of the

state-of-the-art TIA filter topology. Figure 2.3 a-b) TIA topologies are first order filter, and the

dual real-pole filter respectively, which are quite different from the latter two and from the

proposed design. Therefore, comparing with the Tow-Thomas and Rauch Filter structures shown

in Figure 2.3 c-d) in terms of input impedance will be the main focus in this section.

All of these filters have utilized the advantage of the virtual ground of the Op-Amp. Current

going into the virtual ground node will have a small voltage swing due to the size of the input

capacitance at high frequencies. This voltage swing at the input node divided by the current is

the actual input impedance at that frequency.


First of all, to better compare the input impedance characteristics, it is necessary to study the

shape of the profile and effect on its related parameters. Since all the equations for the filter cut-

off frequencies and Q factors are obtained in the previous section, it is possible to compare all

filter structures assuming they have the same total capacitance (capacitors occupy the most area),

cut-off frequency, quality factor, and in-band gain.

In this case, a total capacitance of 100pF for a fully differential structure is assumed. The filter

cut-off frequency is 3.2MHz (same as in [2]) with a quality factor of 0.707 and in-band trans-

impedance gain is 5kΩ single-ended.

In Figure 2.6, the Tow-Thomas filter has an input impedance expression of:

(2.10)

From (2.10), it can be clearly seen that it is a band-pass shaped input impedance. At DC, the

input impedance is theoretically zero. For band-pass shaped responses, at the resonant frequency,

the maximum value is R3. Next step is to solve equations using equation (2.7) to get the circuit

parameter values for the given specifications:

Table 2.1: Design specifications and circuit parameters for Tow-Thomas Filter

In-Band Trans-Impedance Gain 5 kΩ

Cut-off Frequency f-3dB 3.2 MHz

Quality Factor 0.707

R1 5 kΩ

R2 1.24 kΩ

R3 0.88 kΩ

C1 40 pF

C2 10 pF


Table 2.1 summarized the computed parameters values for the Tow-Thomas Filter to meet the

same design specifications as the other filters. Figure 2.8 shows that the input impedance of the

Tow-Thomas structure is indeed band-pass shaped with peak value equal to R3, and it is mainly

limited by the size of R3 and other circuit parameters but increasing GBP ωt of the Op-Amp will

not improve the in-band input impedance.

In Figure 2.7, the Rauch Filter’s input impedance is somehow equivalent as a RLC resonant

circuit [2]. The inductance L is synthesized by the gyrator R1 and the integrator 1/R2C1. At low

frequency, the inductance creates a virtual ground while beyond the cut-off frequency the input

impedance is set by the grounded capacitance Cs. At the cut-off frequency, the circuit resonates

so the inductance and capacitance cancel out. The input impedance reaches its maximum which

is equal to R2. The input impedance expression is:

(2.11)

Figure 2.8: Bode Plot – Input Impedance of Tow-Thomas Filter with varying GBP

1M 10M 100M100K

Frequency (Hz)

1G

60

0

Gai

n (

dB

Ω) 40

20

10

30

50


Since the ground Cs capacitance in fully differential structure is half sized (when placing the

capacitor between the differential inputs), the Rauch filter input capacitance can be a few times

bigger than the other structures when computing the single-ended values for the same design

specifications, but total capacitances still add up to 100pF.

Table 2.2: Design specifications and circuit parameters for Rauch Filter

In-Band Trans-Impedance Gain 5 kΩ

Cut-off Frequency f-3dB 3.2 MHz

Quality Factor 0.707

R1 5 kΩ

R2 252.5 Ω

C1 13.4 pF

Cs 146.4 pF

Figure 2.9: Bode Plot – Input Impedance of Rauch Filter with varying GBP

1M 10M 100M100K

Frequency (Hz)

1G0

Gai

n (

dB

Ω)

40

20

10

30

50


From equation (2.11), the band-pass shaped input impedance reaches its maximum

(R1R2)/(R1+R2) which is exactly R1 in parallel with R2. If R1 >> R2, the impedance is

approximately equal to R2. From Figure 2.9, it shows that the change in GBP ωt of the OP-Amp

only has a small effect on the peak value and cut-off frequency of the impedance curve. From the

plot and Table 2.2, it can be verified that when R1 >> R2, the maximum value is certainly R2. So

the input impedance of the Rauch filter is mainly limited by the circuit parameters as well. Now,

it seems that Rauch structure is much better than the Tow-Thomas structure in terms of input

impedance when taking the same total capacitance utilizing the advantage in differential

structure.

2.4 TIA Noise and Comparison

Analog integrated circuits (IC) often have many different performance criteria to that must be

met to achieve the required specifications [5]. Noise often limits the value of the smallest useful

signals, and linearity often limits the largest useful signals that can occur in the circuit. Therefore,

linearity and noise together determines an important term - dynamic range (DR) of a circuit. The

Spurious-Free Dynamic Range (SFDR) of a circuit or a system is defined to be the range

between the small detectable signal (i.e. when power of the signal is slightly above the noise

level), and the largest signal without creating detectable distortions (i.e. when power of distortion

power equals to the noise power) in the bandwidth of interest [5]. This section will focus on

studying the noise of the state-of-the-art TIAs.

The total amount of noise introduced by typical filters is generally proportional to kT/C and in-

band integrated noise is more critical in filter designs. Once the noise floor level is defined, the

amount of total capacitance is roughly set. Therefore, it is better to compare these filters in terms

of noise with the same total amount of capacitance as did in the previous section. In theory, these

noise sources have their own transfer functions which can be studied in detail to better get a

sense what the overall output noise should be.

Figure 2.10 shows the Tow – Thomas structure along with its noise sources which are mainly

from the resistors and op-amp noises, including thermal noise and flicker noise. Noise Transfer

functions of the Tow-Thomas Filter at the output due to each noise elements are listed from

equation (2.12) to (2.16). Figure 2.11 shows the bode plots for these transfer functions. The noise

performance of this structure is poor, since all noise elements exhibit a flat in-band noise shaping


and low-pass shaping out-of-band. Notice that in the bode plot shown in Figure 2.11 b) and e),

the zero and pole cancelled each other so the roll-off in the filter stop-band is only -20dB/dec.

Most of the in-band gain are higher than 0dB (i.e. Figure 2.11 b) to e)) which means that the

noise will be amplified and pass onto the next stage. The overall output noise (sum of the noise

transfer functions) will have a flat shaping in-band with a positive DC gain in dB excluding the

flicker noise at low frequency.

(2.12)

(2.13)

(2.14)

C1

R3

C1

R3 R1

VOUT

R2

C2

R1

C2

R2

OP2OP1

VnR12

VnR22

VnR32

Vnop22Vnop1

2

From Mixer

Figure 2.10: Tow-Thomas Filter with Noise Sources


(2.15)

(2.16)

1M 10M 100M100KFrequency (Hz)

(a) |VOUT / VnR1|2 Output Noise Transfer Function

1G

Gai

n (

dB

)

-20

-60

-100

-40

0

-80


(b) |VOUT / VnR2|2 Output Noise Transfer Function

1G

Gai

n (

dB

)

0

-20

-10

10

-30



(c) |VOUT / VnR3|2 Output Noise Transfer Function

1G

Gai

n (

dB

) -20

-60

-40

0

-80


(d) |VOUT / VnOP1|2 Output Noise Transfer Function

1G

Gai

n (

dB

)

0

-20

-10

10

-30

Figure 2.11: Tow - Thomas Filter Noise Transfer Functions with Each Noise Source


(e) |VOUT / VnOP2|2 Output Noise Transfer Function

1G

Gai

n (

dB

)

6

2

4

8

0

10

12

14


For Rauch filter structure with all the noise elements included as shown in Figure 2.12, equations

(2.17) to (2.19) are the noise transfer functions at the output due to each elements, while Figure

2.13 shows the bode plot of each noise element with the same parameter sizes (assuming a total

capacitance of 100pF). Noise due to R1 is flat in-band which is same as the signal transfer

function while noise due to R2 and the op-amp are high-pass shaped in-band due to the zero at

R1Cs. The high-pass noise shaping mechanism in current filters explained in [5] would help to

contribute less to the output integrated noise, because it starts with 0dB and go up at 20dB/dec

towards cut-off frequency while most Tow-Thomas filter noise transfer functions start with

R1/R3 (from equation 2.13 to 2.16) that is higher than 0dB. There is a trade-off between in-band

noise and input impedance in both cases. Noise can be reduced by increasing R3 at the cost of a

higher input impedance, while in Rauch filter reducing Cs would also push the zero further to

lower the amplification of the noise but the input impedance (R2) would increase to maintain the

same cut-off frequency and Q factor.

(2.17)

(2.18)

VOUT

Cs CsC1

R1

C1

R1

R2

R2

Vnop2

From Mixer

VnR12

VnR22

Figure 2.12: Rauch Filter with Noise Sources


Frequency (Hz)


1M 10M 100M100K10K

Gai

n (

dB

)

-10

-30

-50

-20

0

-40

-60

Frequency (Hz)


Gai

n (

dB

) 10

-0

5

15

-5

1M 10M 100M100K10K

20

(2.19)


2.5 Summary

Table 2.3: Summary of State-of-the-Art TIA Topologies and Comparison

TIA Structure Figure 2.3 a)

Single pole

Figure 2.3 b)

Two real pole

Figure 2.3 c)

Tow-Thomas

Figure 2.3 d)

Current Driven

Rauch

Selectivity(Stop-

band attenuation )

Low Medium High High

Input Impedance High Medium Medium Low

Linearity Low Medium Medium High

Noise High Medium Medium Low

Area Large Medium Large Small

Power High Medium Medium Low

Figure 2.13: Rauch Filter Noise Transfer Function with Each Noise Source

Frequency (Hz)

(c) |VOUT / VnOP|2 Output Noise Transfer Function

1M 10M 100M100K10K

Gai

n (

dB

)

20

5

10

15

0


This chapter summarizes the state-of-the-art TIAs that are widely used in filter design, especially

for RF current mixers. Table 2.3 shows a rough comparison between these designs in terms of

filter response, input impedance, noise, linearity, area and power consumption. The two biquad

structures that have complex poles called Tow-Thomas and Rauch Filters are studied in detail in

terms of signal transfer function, input impedance, and noise. To have a fair comparison, the

parameters in the structures are sized to have the same total capacitance, cut-off frequency and

Quality factor. Both structures have an advantage that they are easily reconfigured. However, in

fully differential structures, Rauch filter has the advantage that the capacitor to ground can be

half-sized and connect both terminals to common-mode, which results in a lower input

impedance. The noise of the Rauch filter also benefits from the in-band high-pass shaped transfer

functions which is also better than the Tow-Thomas filter. The linearity of the Rauch filter can

be improved by tuning the single op-amp while Tow-Thomas filter has two op-amps and the

second op-amp needs to be more power hungry. In conclusion, Rauch filter is the better state-of-

the-art TIA structure.

CHAPTER 3. PROPOSED TRANS-IMPEDANCE AMPLIFIER 21

Chapter 3

Proposed Trans-Impedance Amplifier

3.1 Structure and Transfer Function

In Figure 3.1, the filtering TIA in [3] is presented. The basic idea of this reference design is to

use the active feedback network that contains three zeros, two at DC and one at R2C2, to connect

to the single pole feed-forward loop, so this will allow a sharper transition between in-band and

out-of-band regions thus increasing the order of the closed-loop filter response. The design in [3]

only aimed to achieve large interferer attenuation out-of-band and high 1-dB compression point

where the maximum input current it can handle is 10mA out-of-band. The total current

consumption in [3] is 17mA and total capacitance used is in hundreds of pF (area times

capacitance density).

CIN CIN RF

RF

R2

C3 C3 C1 C1

R2

CF

CF

R1 R1

IIN+

IIN-

VOUT-

VOUT+

R2

C2

R2

Figure 3.1: Original Filtering TIA with active feedback network


The proposed design uses the similar idea as in [3]. In order to have two complex poles in the

closed loop transfer function to obtain a 2nd

order low-pass profile, two real zeros are needed in

the feedback network as shown in Figure 3.1. One zero is at DC implemented by C1, and one is

at 1/R2C2 implemented in the feedback network with a class-AB operational trans-conductance

amplifier (OTA) to achieve the adaptivity. In the filter pass-band, the filter works as a

conventional TIA with the trans-impedance gain set by the feedback resistor R1 because both

capacitor C1 and C2 are high impedance at low frequency. On the contrary, in the filter stop-band,

the capacitance C1 is boosted by draining the high-frequency component of the input current

interferer (IINT) before entering into the virtual ground of the feed-forward Op-Amp (ITIA).

Theoretically, the capacitor C1 can absorb out-of-band interferers without any swing at the input

of the TIA, which ensures a low input impedance to improve the linearity of the passive mixer.

Furthermore, since one of the terminals of C1 is connected to the output of the OTA in the

feedback network, it can easily swing rail-to-rail without affecting the input swing on the other

side of the terminal of C1. Due to this property, the size of the capacitor C1 to absorb a given

amount of input current can be much smaller compared to the other state-of-the-art filters

discussed in chapter 2 where the voltage swing at the input of the TIA followed by a current

passive mixer is usually limited to a few hundreds of mV.

RF VOUT

Cs CsR1

R1

MixerIIN

R2

C1 C1

C2

C2

C2

R2 C2

ITIA

IINT

Figure 3.2: Proposed Filtering TIA with Adaptive Feedback Network


The transfer function of the proposed design is as the following:

(3.1)

{

√

√

(3.2)

The proposed design has a similar form in terms of transfer function in equation (3.1) as the

other filters mentioned in Chapter 2. The filter cut-off frequency is defined by the two time

constants R1C1 and R2C2. The quality factor Q is a ratio of the two time constants. In order to

make the filter a biquad, Q is set to be equal to 0.707 to achieve the flattest passband frequency

response with no peaking or no overshoot in the step-response. The proposed TIA is targeted to

achieve the same cut-off frequency and quality factor as the Rauch Filter in [2] which is 3.2MHz

to address WCDMA standard which is 1.92MHz channel bandwidth, and 0.707 respectively to

better compare the two designs in terms of area, noise, and input impedance essentially.

Transfer functions of TIA current and Interferer current over Input current of the proposed

design:

(3.3)

(3.4)


The low-pass shape of ITIA/IIN and high-pass shape of IINT/IIN are clearly shown in Figure 3.3 and

their transfer functions in equation (3.3) and (3.4) respectively. The two zeros in the feedback

network can be clearly seen in equation (3.4). Within the pass-band, the amount of interferer

current IINT drained by capacitance C1 is increasing 20dB/dec towards the filter cut-off frequency

ω0. In the filter stop-band, all the input current should be drained by the capacitance C1 ideally,

since ITIA attenuates at high frequency following the signal transfer function (STF).

Figure 3.3: Bode plot - Transfer function of TIA current and Interferer current over Input

current

1M 10M 100M100K

Frequency (Hz)

I TIA

/IIN

(d

B)

I IN

T/I

IN (

dB

)

1M 10M 100M100K

Frequency (Hz)


3.1.1 Finite Trans-Conductance and Gain Bandwidth Product

The transfer function is shown in the previous section with ideal components (infinite GBP of

the feed-forward Op-Amp, and infinite trans-conductance OTA). However, in fact, the OTA in

the feedback network introduces a pair of complex conjugate poles in the feedback network due

to finite trans-conductance gm, which become a pair of complex zeros in the closed-loop transfer

function. The new transfer function now becomes:

(3.5)

{

√

√

√

(3.6)

As shown in the equation (3.5), the finite trans-conductance gm indeed introduced two complex

zeros in the closed-loop transfer function, which is located at ωz. It can be seen from equation

(3.6) that the cut-off frequency ω0, ωz and quality factor Q become functions of gm now. It is

crucial to analyze the impact due to the finite trans-conductance gm introduced to the system.

First, the simplest equation in (3.6) is the zero location ωz which is directly proportional to the

trans-conductance gm. Therefore, it sets a constraint when choosing the value for the gm. The

zeros have to be placed at least one decade (10 times) after the filter cut-off frequency to keep

the in-band response flat, to obtain a larger attenuation after one decade with -40dB/dec roll off

and to be independent of the magnitude of the out-of-band interferers. With trans-impedance

gain of 5kΩ, it sets a constraint for the gm:

√ 20 mS (3.7)


In (3.6), the quality factor now becomes much complicated to see the impact with the finite gm,

but the value gets closer to 0.707 as gm increases shown in the following plot Figure 3.4.

The impact on the Quality factor of the circuit due to finite trans-conductance gm is plotted in

Figure 3.4. This plot is obtained by keeping all the other parameters (i.e. resistors and capacitors)

the same, and from the plot, the minimum gm required to keep the quality factor within 3% from

the ideal value is 20mS with Q equal to 0.69.

To see the effect on the filter cut-off frequency ω0, in the denominator, left side should be much

bigger than the right side

(3.8)

By substituting the gm with 20mS into equation (3.8), the left side is indeed more than one

hundred times bigger than the right side.

Figure 3.4: Quality Factor as a Function of varying Trans-Conductance gm

Qu

alit

y F

acto

r

Trans-Conductance gm (Siemens)


Figure 3.5 is a bode plot that shows the finite trans-conductance gm provided by the OTA that

can be used to adjust the location of the complex zeros in the closed-loop transfer function. (i.e.

ωz increases as gm increases from 10mS to 50mS). Notice that as the gm increases, it behaves

more as a notch filter at that particular narrow frequency range with a high Quality factor thus

improving the filter selectivity with more attenuation, but when the response goes back up

reducing the attenuation, the power on the OTA can be mainly controlled to provide higher trans-

conductance to get the required out-of-band attenuation according to different design

Figure 3.5: Bode plot –Transfer Function and Phase Response of the TIA with Increasing

Trans-Conductance gm

1M 10M 100M100K

Frequency (Hz)

1G

70

60

50

40

30

20

Gai

n (

dB

Ω)

0

-25

-50

-75

-100

-125

-150

Ph

ase

(Deg

ree)

1M 10M 100M100K

Frequency (Hz)

1G

ωz

ωzωz

40 dB


specifications. This adds a degree of freedom in design optimization. As mentioned above, gm

has to be at least 20mS to have a minimum impact to keep the filter cut-off frequency and quality

factor. In Figure 3.5, gm is verified to be at least 20mS to have the zeros one decade after the

filter cut-off frequency and a -40dB attenuation at higher frequencies shown in the plot.

Therefore, the minimum requirement for the trans-conductance gm of the OTA is defined.

Now, the finite GBP ωt of the Op-Amp in the feedforward path has to be taken into account. The

transfer function considering only GBP ωt of the Op-Amp now becomes:

(3.9)

As discussed above, if the trans-conductance gm is infinite, the complex zeros are at infinity

which is not the real case. From transfer function (3.9) excluding finite gm, it can at least help to

define the minimum GBP ωt of the Op-Amp to have minimum impact on the closed-loop transfer

function,

{

(3.10)

Since the target of the filter cut-off frequency should be able to configure from WCDMA

standard to LTE20 standard 10MHz, the Op-Amp GBP ωt has to be sufficient large to satisfy the

equation (3.10). Now, considering all finite parameters including trans-conductance gm, GBP ωt

and also the second pole ωp2 of the op-amp, the input shunt capacitor to ground Cs is now useful

to drain the very far-away interferers when the loop gain of the op-amp drops. The overall

transfer function becomes more complicated to show and analyze. Figure 3.6 shows the overall

transfer function bode plot with increasing in gm as in Figure 3.5. The op-amp finite parameters

and Cs together created more complex poles resulting in a steeper roll-off at high frequencies

which improves the selectivity. A few dB peaking effect is due to the notch effect created by the

gm as shown in Figure 3.5 and shunt capacitor along with finite GBP of the op-amp together. In

later sections, it will discuss the stability of the peaking effect and introduce a way to bias the

OTA to lower the peaking effect and an adaptive transfer function will be realized.


1M 10M 100M100K

Frequency (Hz)

70

60

50

40

30

20Gai

n (

dB

Ω)

10

0

Figure 3.6: Bode plot –Transfer Function and Phase Response of TIA With Real Parameters

Phas

e (D

egre

e)

1M 10M 100M100K

Frequency (Hz)

100

50

0

-50

-100

-150


3.1.2 Reconfigurable TIA Filter

Another target of the TIA is to be reconfigurable between WCDMA standard and LTE standard

up to 20MHz optimistically. Unit sized capacitors are used to build up the capacitor banks for re-

configurability. Simple MOS switches will be used to control all these binary weighted

capacitors. Therefore, minimizing the number of tuning parameters should be the primary goal to

save more pins on the pad and area consumed by the MOS switches. The circuit now introduces

a constant α which is a multiplier of the first C2 in the feedback network as shown in Figure 3.7.

The circuit transfer function and its associated parameters become the following:

(3.12)

RF VOUT

Cs CsR1

R1

MixerIIN

R2

C1 C1

C2

αC2

αC2

R2 C2

IINT

Figure 3.7: Proposed Filtering TIA with Reconfigurable Cut-off Frequency


{

√

√

√

(3.13)

From equation (3.12) and (3.13), it is clear that the constant α does not affect any of the

equations but a simple multiplying constant. In this way, it saves more pins and area instead of

tuning every parameters of the filter which will limit the circuit performance since the MOS

switches will introduce parasitic capacitances and small-signal resistance in triode region. In the

receiver chain, the low-noise amplifier (LNA) and mixer together provide a trans-conductance of

about 40mS, thus the overall gain of the receiver chain sets the TIA gain to have a very low

tuning range regarding to the specifications. The location of the zeros will be always at least one

decade after the poles as seen in equation (3.7) if R1 is fixed and gm > 20mS. So the circuit

tuning is done by varying R2, C1 and α. In order to keep the same quality factor in (3.13), since

R2 is in the numerator, αC1 in the denominator must decrease the same multiplier as R2. By

rearrange these equations, it is possible to get the equations among these circuit parameters, such

as the following:

{

(3.14)


Figure 3.8 shows the reconfigurable TIA bode plot tuned from 3.11MHz to 16.9MHz taking all

the non-ideal parameters into account with gm = 20mS , ωt much greater than in (3.10), and

varying Cs by scaling R2, α, and C1 while keep other parameters and the quality factor the same.

1M 10M 100M100K

Frequency (Hz)

60

0

Gai

n (

dB

Ω)

40

20

10

30

50

70

f-3dB= 3.11MHz

f-3dB= 16.9MHz

Figure 3.8: Bode Plot –Transfer Function of Amplitude and Phase Response with Re-

configurable Cut-off Frequency

Ph

ase

(Deg

ree)

f-3dB= 3.15MHz

f-3dB= 15.8MHz

-250

100

50

0

-50

-100

-150

-200

1M 10M 100M100K

Frequency (Hz)


Among the tuning ranges, the entire plots exhibit the same biquad behaviour with -40dB/dec roll

off after the cut-off frequency and the quality factor for all these cases are Q ≈ 0.707. The reason

why the highest bandwidth cannot achieve 19.1MHz with the theoretical equation (3.2) is

because the fixed finite gm and GBP ωt at 200MHz affects the transfer function more

significantly than the lowest bandwidth case, but the gain peaking effect with higher bandwidth

is less since the complex zeros are already at high frequency and Cs takes into account regarding

to ωt. Moreover, it can be verified in the plot that complex zeros are always one decade after the

cut-off frequency due to the finite gm which is 20mS. This enhances the advantage that

controlling the zeros not only improves the selectivity but will not affect the in-band response or

the cut-off frequency. Finally, the shunt capacitor Cs could be a few times smaller than the Rauch

filter and it will not affect the in-band response thus providing another degree of freedom to tune

the filter according to different bandwidths and specifications. Table 2.1 below summarizes the

design specifications and circuit parameters used in Figure 3.8.

Table 2.1: Design Specifications and Circuit Parameters for the Reconfigurable TIA

Cut-off Frequency f-3dB

(MHz) (in Figure 3.8)

3.11 6.11 8.77 11.87 14.27 16.9

Quality Factor 0.700 0.697 0.683 0.688 0.682 0.683

Op-Amp GBP ωt (MHz) 50 80 110 140 170 200

OTA gm (mS) 20 20 20 20 20 20

In-Band Gain R1(kΩ) 5 5 5 5 5 5

R2 (kΩ) 5.86 2.93 1.95 1.465 1.172 0.977

C1 (pF) 14 10.5 11.5 10.5 11.5 9.5

C2 (pF) 6 6 6 6 6 6

αC2(pF) 6 4 2.5 2 1.5 1.5

Cs Single-Ended (pF) 48 24 24 12 12 6

Total Capacitance - Fully

Differential (pF) 100 85 69 59 59 52


3.2 Input Impedance

(3.15)

Since the input of the proposed TIA is directly connected to the virtual ground of the Op-Amp, at

low frequency, the impedance should be zero in theory. Equation (3.15) shows the input

impedance of the TIA is not zero when finite GBP ωt is considered. It is also a band-pass shaped

and at the cut-off frequency, the maximum value should reach 1/(αC1ωt) by simplifying equation.

The input impedance plot for the WCDMA base case with cut-off frequency at 3.2MHz is shown

in Figure 3.9. The full transfer function equation is too complicated to show, so the graph has

intuitively shown the effect on the input impedance curve due to each parameter in the filter

including ωt, Cs and gm. The first zero is at DC, and the peak value of the band-pass shaped

curve has more effect when increasing the GBP ωt. The finite trans-conductance gm has

introduced a pair of zeros which causes a 20dB/dec rising after the peak which is due to the first

two poles. In order to make the input impedance low-pass shaped, the shunt ground capacitance

Figure 3.9: Bode Plot – Input Impedance Transfer Function of Proposed TIA Filter with

Varying Parameters

1M 10M 100M100K

Frequency (Hz)

1G0

Gai

n (

dB

Ω)

40

20

10

30 ωt

gm

Cs


Cs has to play an important role to lower the input impedance at high frequency which introduces

two poles around the zeros location. The final input impedance transfer function including these

non-ideal parameters should have 4 poles and 3 zeros.

Notice that the Cs capacitance is only 48pF, other capacitance C1,C2 only contribute 52pF while

in the Rauch Filter Cs is 146pF which is 3 times bigger, and the maximum impedance level is

higher as well. Therefore, using same amount of total capacitance in these structures, the

proposed TIA has the lowest input impedance. In other words, for the other filters (Tow-Thomas

and Rauch) to get the same level of input impedance as the proposed TIA, the capacitances

needed (the area) would be much bigger. The ωt requirement which is directly related to power

consumption of the Op-Amp in other designs may not be as strict as the proposed design.

Since the maximum input impedance level is related to 1/(αC1ωt), it has an interesting

characteristic when reconfiguring the filter frequency. Bring back the equations in (3.13) for the

filter cut-off frequency and quality factor, it can be noticed that scaling R2, α, and C1 as in the

previous subsection would have the lowest number of tuning parameters while keeping the in-

band gain R1 and the quality factor the same for all bandwidths. However, considering the max

input impedance, 1/(αC1ωt) will now be increasing since αC1 is scaled down for higher

bandwidth. In the following Figure 3.10 a), it shows that the max input impedance level

increases as the bandwidth of the filter increases by scaling down R2, α, and C1. Another option

to re-configure the filter to keep the same quality factor and low input impedance is by scaling

down R1, R2 and both C2 to keep the lowest input impedance possible as shown in Figure 3.10 b).

This option can be used if there is a strict specification on the input impedance and a low in-band

gain is needed. This is the trade-off between input impedance and in-band gain when tuning the

circuit. The trade-off for low input impedance in other state of the art filters discussed in Chapter

2 mainly comes at the cost of area (input capacitance and size of the resistor), while the trade-off

in the proposed design mainly comes from the finite gain bandwidth of the op-amp which is the

power.


1M 10M 100M100K

Frequency (Hz)

(a)

1G

Gai

n (

dB

Ω)

40

20

10

30

50

f-3dB= 3.11MHz Case

f-3dB= 16.9MHz Case

Figure 3.10: Bode Plot – Input Impedance of Proposed TIA Filter with Reconfiguring

Bandwidth and Scaling Options

1M 10M 100M100K

Frequency (Hz)

(b)

1G

Gai

n (

dB

Ω)

30

10

0

20

f-3dB= 3.11MHz Case

f-3dB= 16.9MHz Case


3.3 Spurious-Free Dynamic Range

3.3.1 Noise Transfer Functions and Analysis

(3.16)

(

)

(3.17)

VOUT

R1

R1

R2

C1 C1

C2

C2

C2

R2 C2

From Mixer

VnR12

Vnop2

OP

VnR22

Vngm2

Figure 3.11: Proposed TIA Filter with Noise Sources


(

)

(3.18)

(

)

(3.19)

Equation (3.16) is the noise transfer function from R1 to the output. It is clear that it behaves the

same as the filter transfer functions which is a flat band shaping in-band since the trans-

impedance resistor R1 will simply amplifies the noise along with it. For equation (3.17) to (3.19),

it is obvious that there are zeros in the numerator which means it is a high-pass shaped in-band

response.

It can be understood intuitively from Figure 3.11 with the noise sources appeared in the circuit

diagram. At low frequencies, the capacitor C1 and C2 are high impedance, there is no noise

injected into the feedback network, and the noise generated by the noise sources in the feedback

network cannot be injected into the feed-forward path, thus reducing the total output noise at low

frequency. In the bode plot Figure 3.12 b) and d), these can be verified that the first zero is at DC,

therefore the transfer function plot starts below 0dB and rise up at 20dB/dec towards the cut-off

frequency.

The plot is generated by reconfiguring the TIA as done in subsection 3.1.2. When reconfiguring

the TIA, αC1 and R2 is scaled down mostly while R1 stays constant, thus making the complex

poles moving further. The first zero at C1R1 will keep rising until the cut-off frequency. This

unique property offers more benefits to the noise performance compared to the other two designs,

because the high-pass shaped noise sources contribute a lot less (below 0dB) than the Rauch

Filter (starts with 0dB). Therefore, excluding the flicker noise, the overall output noise transfer

function of the TIA will be mostly flat in-band for the lowest bandwidth configuration, while the

noise shaping will be slightly going up above 0dB for the highest bandwidth configuration as

shown in Figure 3.12. All the high frequency peaking due the finite GBP ωt and trans-

conductance gm is negligible since in-band noise shaping is the most important in terms of noise

performance.




Gai

n (

dB

)

-10

-30

-20

0

-40



Gai

n (

dB

)

0

-20

-10

10

-30


Frequency (Hz)

(c) |VOUT / VnOP|2 Output Noise Transfer Function

Gai

n (

dB

)5

-10

0

-5

10

1M 10M 100M100K

Figure 3.12: Proposed TIA Filter Output Noise Transfer Function with All Noise Source

Frequency (Hz)

(d) |VOUT / Vngm|2 Output Noise Transfer Function

Gai

n (

dB

) 0

-20

-10

10

1M 10M 100M100K


3.3.2 Linearity and Intermodulation Phenomena

Due to the same reason and the unique property of the proposed TIA filter, the intermodulation

product (IM) generated in the filter passband should also follow the high-pass shaping as the

noise transfer function shown in Figure 3.13. Since the out-of-band interferers are drained by the

capacitance C1 instead of going into the feed-forward path, the IM product generated in the filter

passband due to these interferers is also high-pass filtered by C1, thus providing a high linearity

within the filter pass-band. The filter linearity will be mostly limited by the op-amp if there is

already IM products in the pass-band at the input, but it will not be limited by the feedback

network and the OTA.

R2 C2

C2

C2

R2 C2

C1

C1

IINT

TIA

Virtual

Ground

TIA

Output

ω1 2ω1- ωIM3ωIM3 3ω1- 2ωIM3

Pass-band Interferers

ω

Mag

nit

ud

e

ω1 2ω1- ωIM3ωIM3 3ω1- 2ωIM3

Pass-band Interferers

ω

Mag

nit

ud

e

Figure 3.13: Proposed TIA Filter Intermodulation Product Phenomena


3.4 Stability Analysis

The proposed TIA filter has a few feedback networks as shown in Figure 3.14. In the main loop,

the feedback network consists of the OTA and the zeros created by C1 and R2C2. In the inner

loop 1, around the Op-Amp, the feedback is mainly the trans-impedance resistor R1. In the inner

loop2, around the OTA, the feedback network mainly consists of R2C2 in series. While doing

loop gain analysis, a test source should be inserted in the breaking points shown in Figure 3.14,

so the loop gain will be equal to -Vrx/Vtx [5]. In Figure 3.15, the theoretical bode plot shows the

loop gain for the main loop. At low frequencies, the zero due to capacitor C1 provides the high

pass shaped 20dB/dec rising with a phase of -90 degree. Another zero due to R2-C2 provided by

the inverting structure around the OTA is introduced causing an increase in phase change while

the op-amp finite bandwidth ωt, the second pole ωp created complex poles causing the phase to

drop dramatically while the gain drops with almost -60dB/dec up to 1GHz. The phase margins at

the two zero crossing point are maintained more than 90 degrees since the OTA’s finite

bandwidth is not modelled in the theoretical bode plot. A few dB gain peaking in the closed-loop

transfer function in Figure 3.6 is mainly due to this phase margin but can be compensated by the

VOUT

R1

R1

R2

C1 C1

C2

C2

C2

R2 C2

From Mixer Vt1Vr1

Vt2 Vr2

Vr3 Vt3

Loop 1

Loop 2

Main Loop

Figure 3.14: TIA Loop Gain Analysis – All Breaking Points


grounded input capacitance Cs. As Cs increases shown in Figure 3.15, it moves the dominant pole

to lower frequency which is created by the op-amp finite gain bandwidth ωt,, and improves the

phase margin of the open loop gain. Therefore, the gain peaking does not compromise the

stability, but it can be easily controlled by adding more input capacitance. The detailed stability

analysis will be studied in Chapter 4 with transistor level implementations.

Figure 3.15: TIA Loop Gain Analysis – Overall Loop Gain Bode Plot

100K 10M 100MFrequency (Hz)

1G

Gai

n (

dB

)

20

-40

0

-20

40

1M

-60

Cs

Ph

ase

(Deg

ree) -100

-200

-150

-50

-250

100K 10M 100MFrequency (Hz)

1G1M


3.5 Adaptive Filtering Response

Due to the filtering effect provided by the input capacitance C1, it is possible to implement the

OTA in the feedback network biased with a small dc current to work in class-AB output stage

while still maintaining a high linearity, low noise but uses much less power than class-A circuit.

In this way, in the absence of large out-of-band interferers, the OTA still works in class-A with

sufficient gm to maintain a good selectivity. In the presence of large out-of-band interferer

current IINT drained by C1, the OTA starts to work in class-AB thus providing higher trans-

conductance gm proportional to the magnitude of the interferer current. The output of the OTA

will have a large swing, even rail-to-rail, while the input swing will still be within a few hundred

mVs when the TIA is not compressing. Figure 3.16 below shows the bode plot with increasing

gm as in Figure 3.6. The dashed lines are the trend of the adaptive transfer function as the

magnitude of the interferer current increases. This unique characteristic allows changing the

filter selectivity automatically without the need of any control loop, therefore adding another

degree of freedom in the design optimization.

Figure 3.16: Bode Plot – Adaptive Transfer Function Sketch of Proposed TIA with Increasing

Interferer Power (Theoretical)

1M 10M 100M100K

Frequency (Hz)

70

60

50

40

30

20Gai

n (

dB

Ω)

10

0


3.6 Summary

This chapter introduced the original TIA topology idea from the reference design and described

the major modifications in this design. It studied the proposed design in terms of ideal transfer

function, effect of the finite trans-conductance gm, input impedance, noise transfer functions and

linearity. Finally the stability of the loop gain is analyzed, and an adaptive filtering profile can be

achieved by using a class-AB OTA in the feedback network to achieve the adaptivity.

CHAPTER 4. SYSTEM AND CIRCUIT DESIGN 46

Chapter 4

System and Circuit Design

This chapter outlines the circuit implementation in transistor level of the proposed TIA. It

introduces the implementation of the main op-amp and summarizes the advantages and

disadvantages biasing the CMOS inverter OTA in class-A and class-AB; also binary capacitor

banks with MOS switches. The stability of each feedback loop is simulated, including the

common mode feedback loop. The final simulation results are presented at the end of this chapter.

4.1 Operational Amplifier in Feed-Forward Path

From the previous chapter, the most important specification of the op-amp is defined which is

the GBP ωt to satisfy (3.10) for all tuning bandwidths. The proposed design uses the common

Two-Stage Miller Compensated topology for the main op-amp in the feed-forward path. The

two-stage op-amp can provide a high gain and high output swing which is suitable for the

proposed TIA. There are some other important specifications of the op-amp need to be

determined, such as the dc gain A0, slew rate, and input thermal noise due to the gm.

First of all, the dc gain A0 affects the input impedance mostly at low frequency. From Figure 4.1,

a conventional TIA, it is clearly seen that VOUT = -A0VIN, and is also equal to IINR1. By

simplifying the equations, VIN/IIN = - R1/A0 and it gives the requirement for A0 which is greater

than 34dB if the input impedance requirement is less than 100Ω. However, 34dB is low compare

VOUT

-A0

VIN

IIN

R1

Figure 4.1: Conventional TIA


to moderate two-stage op-amp dc gain; therefore the target should be greater than 40dB.

Secondly, the slew rate limitation of the TIA is not strictly requirement because the input is a

current and going into the virtual ground node. The voltage swing at the input is limited due to a

large finite GBP, therefore the output voltage change will not be limited due to slew rate, but the

target should be moderate such as 100V/μs. Finally, the thermal noise due to the input pair

should be less than a 1kΩ resistor, as in equation (4.1), gm of the input pair is defined to be at

least greater than 1mS.

Ω (4.1)

(4.2)

(4.3)

(4.4)

(4.5)

(4.5)

gm1Vin R1 C1 gm5V1 R2 C2

VOUT

RC CC

V1

Figure 4.2: Small Signal Model of the Two-Stage Miller Compensated Op-Amp


Equations (4.2) to (4.6) and Figure 4.2 in the text book [5] provide the main guidance when

designing the two-stage op-amp. Figure 4.3 is the full schematic for the op-amp with transistor

sizes labelled. The Miller Compensation Capacitor used is 1.3pF, and RC is 1.4kΩ. The first

stage input pair gm is about 1.9mS which ensures the GBP ωt satisfies (3.10) with equation (4.3).

The bias current used in M9 and M10 is 200µA which makes the slew rate of the op-amp with (4.5)

is greater than 100 V/μs. The noise of the input pair is less than a 1kΩ resistor since the input gm

is almost twice than the calculated value. The input pair W/L ratio is made large enough to have

the transistors work in subthreshold region to achieve the highest gm efficiency for a given

amount of current. Notice that the second stage transistors do not have to be big and consume a

few times more current than the first stage, because the capacitive load αC2 it drives decreases as

the filter bandwidth is tuned larger. Therefore, the second pole location (4.4) is moved far away

to make the Op-Amp more stable and gain more phase margin. The size of M5 is twice as M3

thus the second stage consumes 200µA current, with roughly twice the gm.

R1 R1

VDD

IBIAS

VINP

VDD

VOUTP

VINN

VOUTN

VDD VDD

VCMFB VCMFB

VOUTP VOUTN

VCMFB

VREF

M1

M3M5

M7

M2

M4 M6

M8M9 M10

RC CC RCCC

Transistor Sizing in µm W/L

M1,M2 120/0.2

M3,M4 20/1

M5,M6 40/1

M7,M8 20/0.2

M9,M10 10/0.2

R1 R1

R1 R1

OP1

Figure 4.3: Two-Stage Miller Compensated Op-Amp for the Proposed TIA


Length of M3 and M4 are also sized large enough to lower the flicker noise contributed to the

output while increasing the length improves the gain as well. R1 in Figure 4.3 are all 100kΩ for

the common mode signal and it is sized 20 times larger than the feedback trans-impedance gain

resistance in the TIA to minimize the impact to the equivalent resistance seen at the output node.

Notice that the common mode feedback signal is connected to the PMOS in the second stage

instead of the first stage due to stability issues, since the common mode gain is too large when it

feedbacks to the first stage and it is harder to compensate. Therefore, putting the common mode

feedback node in the second stage is a better option while still achieving a good accuracy of

sensing the common-mode signal (a few mV difference). The current consumption for this

common mode feedback circuit is 15µA.

The total simulated current consumption for the op-amp is approximately 615µA. The open-loop

dc gain is 47dB with a phase margin of 50 degree and a GBP of 104MHz for the lowest

bandwidth case. Since the loading capacitance is the largest with a cut-off frequency of 3.2MHz,

100MHz GBP is large enough to meet the requirement (3.10) in Chapter 3 without affecting the

in-band transfer function. At the other extreme, the GBP is 210MHz for the highest bandwidth

case with the smallest loading capacitances.

VINP VINN

VDD VDD

VOUTVDD

IBIAS

M1 M2

M3 M4

M5 M6


M1,M2 11.2/0.12

M3,M4 0.72/0.12

M5,M6 2/0.5

Figure 4.4: Common Mode Feedback Amplifier for Two-Stage OP-AMP


4.2 Operational Trans-conductance Amplifier in Feedback

Network

The OTA in the feedback network can be implemented using a simple CMOS transconductor as

in Figure 4.5 This simple trans-conductor is biased to work in class-A stage only. However, the

dc bias current for this class-A transconductor is large to provide a given amount of trans-

conductance gm since it is proportional to μCoxW/L (VGS – VT) and VG is biased at the common

mode of the circuit which is half VDD. Class-A amplifiers always conduct during one complete

cycle of the input signal waveform thus providing minimum distortions and maximum output

swing. Due to the intrinsic high-pass shaping of the noise and distortion produced by the

feedback network, the distortions generated at low frequencies are filtered out; the OTA can be

biased in class-AB stage without compromising the overall linearity of the TIA and consume less

power in the absence of large out-of-band interferers. The only trade-off is between power and

area since biasing in class-AB stage would result in a small Veff with a very large W/L ratio and

duplicated capacitance C2, αC2 and R2 to provide the same amount of trans-conductance gm (at

least 20mS found in Chapter 3).

VDD VDD

VOUTVINP VINN

Figure 4.5: Simplified Scheme for CMOS Trans-conductor


Figure 4.6 shows the full scheme of the OTA in the feedback network with the biasing circuit. It

can be seen that the input voltages are at different common mode level, one is at the NMOS

input current source VBIAS, and the other one is at the output of the common mode feedback

amplifier OP2 to maintain the OTA output at the common mode level VREF. Consequently, one

drawback of this biasing scheme is an extra input node is required so duplicated C2 R2, and αC2

have to connect to the PMOS and NMOS separately.

However, the VEff voltages of the PMOS and NMOS are reduced by about 200mV so the bias

current can be reduced which is controlled by the NMOS current mirror. The current mirror

NMOS drain voltage is also biased at the common mode level with amplifier OP3 to accurately

control the mirrored current. The W/L ratio of the P,NMOS are made sufficiently big to sustain

the large current coming from the output node connected to the capacitor C1 in the TIA. This

class-AB operation is clearly shown with the transient simulation results in Figure 4.7.

VREF

VDD

VDD VDD

M1 M2

M3 M4

R1 R1

R1 R1

R1 R1

VINPPMOS

VINPNMOS

VOUTPVOUTN

IBIAS

M5


M1,M2 240/0.12

M3,M4 240/0.12

M5 240/0.12

VBIAS

VREF

VBIAS

OP2OP3

VINNPMOS

VINNNMOS

Figure 4.6: Proposed Operational Trans-conductance Amplifier with Bias in Class-A or

Class-AB


a)

Time (ns)

Ou

tpu

t V

olt

age(

V) 1.0

0.4

0.8

0.6

1.2

02 4 60 8 10 12 14 16 18 20

0.2

200 µA

2 mA

b)

Figure 4.7: OTA Output Voltages and Drain Currents with Different Input Current at

50MHz

1.5

0.5

1.0

2.0

2.5

Dra

in C

urr

ent

(mA

)

2 4 60 8 10 12 14 16 18 20

Time (ns)

200 µA

2 mA


Figure 4.7a) and b) shows the output voltages and drain currents respectively, at the node VOUTN

and VOUTP with different input current amplitude simulated at 50MHz labelled with blue and

black traces. From previous chapter, it is known that the zeros are placed one decade after the

filter cut-off frequency which is 3.2MHz. Therefore, at 50MHz the signal should follow the filter

transfer function with the zeros introduced as in Figure 3.5.

The dc bias current is about 400μA in each branch to provide a total trans-conductance of 20mS

to meet the requirement. The black line in Figure 4.7 a) and b) is when input current is small

(200uA) so the OTA is still working in class A. The current drained by the OTA is still a perfect

sinusoid centered at 400μA, and the output voltage swing is small. The blue line is when input

current is large (i.e. 2mA) which is drained by the TIA input capacitor C1 connected to the output

of the OTA, thus forcing the OTA to work in class-AB. The drain current starts to introduce

distortions and a half wave plus a portion of the other half is presented in Figure 4.7 b). The

voltage at the OTA output is almost rail-to-rail while the input voltage swing is still within a few

hundred mV due to the filtering effect provided by C1. The trans-conductance provided by the

OTA is larger when it works in class-AB with large interferer current since it is proportional to

the drain current. In the closed-loop transfer function, the attenuation at that frequency is larger

due to the bigger trans-conductance gm. Therefore, the filter transfer function established a

unique adaptive characteristic depending on the input current beyond frequencies of the zeros

location. The input shunt capacitor Cs also helps to drain the interferer current at very high

frequencies.

VINNVINP

VDD VDD

VOUTVDD

IBIAS

M1 M2

M3 M4

M5 M6


M1,M2 8/0.4

M3,M4 2/0.4

M5,M6 2/0.4

VDD

M1 M2

M5 M6

M3 M4

VDD

VINNVINP IBIAS

VOUT


M1,M2 12/0.12

M3,M4 0.8/0.12

M5,M6 2/0.5

Figure 4.8: Common Mode Feedback Amplifiers for OTA


Figure 4.8 shows the common mode feedback amplifiers used in OTA and their bias currents are

both 5μA. The total current consumption of the OTA is approximately 810μA and it is easily

adjustable with different selectivity requirements.

4.3 Reconfigurable TIA with MOS switches and Capacitor banks

The re-configurability of the TIA is achieved by using a single NMOS switch and binary

weighted capacitor banks with a unit capacitance of 0.5pF shown in Figure 4.9. The NMOS

switch for C1 is placed at the input terminal side because the NMOS can only pass signal up to

VDD - VTH while input voltage swing is limited to a few hundred mV. It cannot be placed on the

other side of C1 because there might be rail-to-rail swing condition. All other switches are all

placed in the proper location with small voltage swings centered at the common mode level. The

W/L ratio of the switch is also checked to be large enough to minimize the RDS introduced.

Figure 4.10 is the top level schematic of the proposed TIA. Although capacitances C2 and αC2

needed to be doubled to be biased in such a way to work in class-A or class-AB, the total extra

capacitance used is only 24pF which is still small compare to the other state-of-the-art filters.

VCTRL

[0:0]

[1:0]

[3:0]

[7:0]

Figure 4.9: Reconfigurable TIA with Switch and Capacitor Banks


RF VOUT

Cs

R1

R1

MixerIIN

R2

C1 C1

C2

αC2

R2 C2

αC2

Figure 4.10: Reconfigurable TIA Top Level Schematic

4.4 Stability Analysis

The loop gain for the main loop of the filter is simulated and phase margins are shown in Figure

4.11 which is similar as the theoretical plot in Chapter 3. The OTA has a finite bandwidth so the

poles in OTA are inverse proportional to the loading capacitance C1 since total gm used is fixed

at around 20mS. For the lowest bandwidth WCDMA case, the zero provided by R2-C2 in the

loop gain is supposed to help gain phase, but the poles in the OTA are also at lower frequency

which cancels the phase improvement due to the zero. However for the highest bandwidth LTE

case, the zero R2-C2 is tuned to higher frequency and the loading capacitance C1 is smaller thus

pushing the poles in OTA at higher frequencies too. The main op-amp bandwidth ωt is not

changed by that much after tuning and is also the dominant pole in the main loop gain so the

phase margin for the highest bandwidth case is automatically improved. The phase margin at the

gain peaking location in the signal transfer function, still has 52 degree of phase margin for

lowest bandwidth case, while for the highest bandwidth case phase margin is 107 degrees so the

peaking effect is reduced shown in Figure 4.15. The grounded input capacitance can be used to

compensate the stability by moving the dominant pole and improve the phase margin but the


total capacitance used in this design is around 100pF, so the amount of input grounded

capacitance used is limited. Therefore, the gain peaking does not compromise the stability but

only reduces the attenuation by a few dB with small out-of-band interferers in the worst case.

The gain peaking effect is further reduced when there are large interferer currents drained by the

class-AB OTA which results in an adaptive filtering profile shown in Figure 4.16. The other

loops are simulated and phase margins of the lowest and the highest bandwidth of typical process

are reported in Table 4.1. Phase margin of all PVT corner simulations are verified above 30

degrees.

Figure 4.11: Bode Plot – Loop Gain of the TIA Main Loop

100K 1M 10M 100M 1G

Gai

n (

dB

)P

has

e (D

egre

e)

-40

0

40

0

-100

-200

-300

-400

Frequency (Hz)

-20

20

PMPM


Figure 4.12: Bode Plot – Loop Gain of the Feed-forward Op-Amp

100K 1M 10M 100M

Gai

n (

dB

)P

has

e (D

egre

e)

0

10

20

30

100

50

0

Frequency (Hz)

WCDMA

LTE

WCDMA

LTE

150

PM

PM

Figure 4.13: Bode Plot – Loop Gain of the Op-Amp Common Mode Feedback

Gai

n (

dB

)P

has

e (D

egre

e)

100

50

0

WCDMA

LTE

WCDMA

LTE

150

PM

PM

100K 1M 10M 100M

Frequency (Hz)

WCDMA

LTE

PM PM

1G

0

10

20

30

40

50

-10

WCDMA

LTE


Table 4.1: Summarized Stability Simulation Results

Lowest Bandwidth Highest Bandwidth

Main Loop (Degree) 52 107

Main Op-Amp (Degree) 48 103

Op-Amp Common-Mode

Feedback (Degree)

100 98

OTA Common-Mode

Feedback (Degree)

96 85

Figure 4.14: Bode Plot – Loop Gain of the OTA Common Mode Feedback

Gai

n (

dB

)P

has

e (D

egre

e)

100

50

0

LTE

150

100K 1M 10M 100M

Frequency (Hz)

WCDMA

LTE

PM

1G

0

10

20

30

40

50

-10

WCDMA

LTE

-20


4.5 Simulation Results

Figure 4.15: Bode Plot - Simulated Reconfigurable TIA Signal Transfer Functions

1M 10M 100M100K

Frequency (Hz)

Gai

n (

dB

Ω)

80

60

40

70

50

30

Δ[email protected]ΔA@95MHz

Figure 4.16: Bode Plot - Simulated TIA Adaptive Transfer Function with Different Input

Signal (cut-off frequency at 3.1MHz)

Small-Signal

7.1 mA

4.0 mA

2.4 mA

1.3 mA

400 μA

240 μA

1M 10M 100M100K 1G

80

60

40

70

50

30

10

20

0

Frequency (Hz)

Gai

n (

dB

Ω)


Figure 4.17: Bode Plot- Simulated Reconfigurable TIA Input Impedance Transfer

Functions

1M 10M 100M100K

Frequency (Hz)

Gai

n (

dB

Ω)

55

45

35

50

40

30

Figure 4.18: Simulated Output Noise – Comparison with State-of-the-Art Designs (

[email protected])

Outp

ut

Nois

e (d

BV

/√H

z)

-130

-135

-140

-145

-150

-155

-160100K 1M 10M10K

Frequency (Hz)

Tow-Thomas

Rauch

This Work

Outp

ut

No

ise

(dB

V2/H

z)


Figure 4.19: Simulated Output Noise – Reconfigurable TIA with High-pass Noise

Shaping

[email protected])

Ou

tpu

t N

ois

e (d

BV

2/H

z)

-170

-135

-140

-145

-150

-155

-160

100K 1M 10M10K

Frequency (Hz)

-165

Figure 4.20: Two Tone Out-of-Band Linearity Test @10MHz and 19.5MHz for Lowest

Band Configuration

-30 -25 -20 -15 -10 -5 0 5 10 15 20

20

0

-20

-40

-60

-80

-100

-120

-140

-160

-180

Δ

PO

UT(d

Bm

)

1 dB/dB

3 dB/dB

PIN(dBm)


(4.6)

The third-order input intercept point IIP3 is calculated without ΔA/2 when the two tones are

placed in-band, where the intermodulation products and the two tones exhibit the same gain.

However, the IIP3 measured in this section is done by placing two out-of-band tones at the

locations specified in Figure 4.15 and Figure 4.16. Since the output power at the tone

location is attenuated by the filter, ΔA/2 has to be taken into account when calculating the

IIP3 of the filter. The first-order output power shown in Figure 4.15 and Figure 4.16 are at

19.5MHz and 95MHz respectively, where it has an attenuation of 32.5dB and 34.5dB

respectively shown in Figure 4.11. Therefore, with the information in Figure 4.15 and Figure

4.16, the simulated IIP3 of the filter is calculated to be 47.25dBm and 34.25dBm respectively.

(4.6)

The Figure of Merit (FOM) defined as in equation (4.7) is used to evaluate filter performance:

(4.7)

Figure 4.21: Two Tone Out-of-Band Linearity Test @50MHz and 95MHz for Highest

Band Configuration

-40 -30 -20 -10 0 10 20

20

0

-20

-40

-60

-80

-100

-120

-140

-160

-180

Δ1 dB/dB

3 dB/dB

PIN(dBm)

PO

UT(d

Bm

)


where Pc is the power consumption of the filter, f-3dB is the cut-off frequency and N is the number

of poles, SFDR is the normalized spurious free dynamic range with equation (4.8):

(

)

(4.8)

where PN is the input referred noise power, integrated over the channel (i.e. WCDMA with

1.92MHz, LTE20 with 10MHz).

Other simulation results including cut-off frequencies for reconfigurable bandwidths, the

adaptive transfer function for the lowest bandwidth configuration, maximum input impedance,

IIP3 and integrated input referred noise for WCDMA and LTE20 are reported in Table 4.2.

Table 4.2: Summary of Simulation Results

Circuit Parameters


R2 (kΩ) 5.86 2.93 1.95 1.465 1.172 0.977

C1 (pF) 14 10.5 11.5 10.5 11.5 9.5

C2 (pF) 6 6 6 6 6 6

αC2(pF) 6 4 2.5 2 1.5 1.5

Cs Fully Differential (pF) 24 12 12 6 4 2


Differential (pF) 100 85 69 59 57 51

Trans-conductance

gm (mS)

20 20 20 20 20 20

Simulated Results


(MHz) (Figure 4.15)

2.96 5.50 7.70 10.08 11.58 13.58

DC Power (mW) 1.68 1.68 1.68 1.68 1.68 1.68

Number of Poles 2 2 2 2 2 2


Maximum Differential

Input Impedance (dBΩ)

(Figure 4.17)

44.2 48 50.5 52 53 55

IIP3 out-of-band (dBm)

(Figure 4.20, Figure 4.21)

47.25 n/a n/a n/a n/a 34.25

Input Referred Noise

Integrated over 1.92MHz,

and 10MHz (µVRMS)

(Figure 4.19)

14.8 n/a n/a n/a n/a 31.8

SFDR out-of-band (dB) 87.2 n/a n/a n/a n/a 74.1

FOM dB(J-1

) 183 n/a n/a n/a n/a 176

4.6 Summary

This chapter summarizes the circuit implementation of the feed-forward op-amp and the class-

AB OTA in the adaptive feedback network. The re-configurability is achieved using capacitor

banks with MOS switches. The stability simulation results are studied and analyzed. All

simulation results are presented and listed in a table.

CHAPTER 5. MEASUREMENT RESULTS 65

Chapter 5

Measurement Results

This chapter summarizes the measurement results of the prototype TIA described in chapter 4.

The PCB setup for transfer function and noise measurement are also shown. The measurement

results compared to other published works are summarized and presented at the end of this

chapter.

5.1 Test Setup

The package chip is placed in a socket which is mounted on a printed circuit board (PCB) for

measurements using laboratory equipment. The PCB is connected through a FPGA (National

Instruments RIO USB-7856R) port which is controlled through LABVIEW interface on a

Windows laptop computer. The input differential voltage signal is fed by a Vector Signal

Generator through SMA connectors, and the differential output is connected to a Spectrum

Analyzer through a differential probe.

5.1.1 Device Under Test

The TIA prototype is fabricated with IBM 0.13μm CMOS technology. The active die area is

about 0.45mm2. The die photo is shown in Figure 5.1 with all the capacitors and amplifiers

labelled. The chip has 32 pins and is packaged using QFN-32. The cavity of the package is about

5mm x 5mm. The dc supply and bias current of the chip is provided by the FPGA through a

voltage regulator and tuned with potentiometer respectively.


5.1.2 Printed Circuit Board

A 4-layer printed circuit board (PCB) and a 2-layer PCB were fabricated to test the packaged

chip. The 4-layer board has two signal layers, an internal power plane and an internal ground

plane. The power plane is split into 4 VDD domains: one is for 5V from the FPGA port; one is

for the chip VDD from the regulator; the other two are for external voltage supplies. The 2-layer

board is for measuring noise with one op-amp, and an instrumentation op-amp. Figure 5.2 shows

the block diagram of the PCBs and Figure 5.3 is the actual photo. A socket for the QFN-32

packaged chip is mounted on the 4-layer PCB. The VDD is provided by the voltage regulator

and the bias currents are tuned with potentiometers. The four SMA connectors are for the

differential input signals coming from the vector signal generator. They are used in pairs for

measuring transfer function and linearity respectively. The input current is generated by feeding

the signal with the voltage signal generator in series with a resistance of 1.6kΩ to emulate the

finite output resistance of the passive mixer (as done in [6]). The output has two pins which are

connected with a differential probe to the spectrum analyzer. For noise measurement, the output

pins have to be connected to the other board, so the amplified noise signal is measured, due to

Figure 5.1: Chip Die Photo

70

0μ

m

680μm

OP

OTA

Cs

C1

Cs

C1

αC2 αC2αC2 αC2

C2 C2C2 C2


the limitation of the instrument itself. With the probe, the noise floor level is higher than the

noise floor level of the filter.

Figure 5.2: Printed Circuit Board Block Diagram

DUTFPGA

Voltage

Regulator

BIAS

Generator

Noise

Measurement

Circuit

Differential

Input Signal

(SMA)

Supply

VoltageSupply

Voltage

Digital Control Signals

Current Bias

Voltage

Feedback

Sensing

Differential

Output Signal

(Probe)

Output

Signal

(SMA)

Differential

Output Signal

External

Power

Supply

Supply

Voltage

Voltage

to

Current

Figure 5.3: Printed Circuit Boards


5.1.3 Equipment Setup

On the laptop computer connected to the National Instruments FPGA, a LABVIEW test bench

has to be setup properly. All the biasing currents and chip total currents are measured with a

small resistor, feeding back the voltages to the FPGA port. The voltages can be reported in

currents on the LABVIEW GUI shown in Figure 5.4 simply by dividing the small resistor

mounted on the board. All other digital control signals and reference common mode signal can

be easily turned on/off on the GUI. The vector signal generator is set up properly to provide

differential signals, and the two tones for linearity test.

5.2 TIA Measurement Results and Comparison

This section presents the measurement results for the TIA prototype, focusing on the transfer

function, input impedance, power, noise, two-tone test, large input signal test, and finally

reported FOMs with different bandwidth and compared with the other published works.

5.2.1 Filter Transfer Function

The filter transfer function is obtained shown in Figure 5.5 by measuring the gains with a small

input current signal (i.e. 40uA), and the re-configurability is achieved by tuning the capacitive

elements of the filter (including the input ground capacitance shown in Figure 5.4 as CS_CTRL).

The frequency tuning range of the TIA measurement is between 2.8MHz and 12MHz to address

cellular applications (i.e. WCDMA, and LTE20). The OTA is biased with 400μA in order to

place the zeros one decade after the filter’s cut-off frequency with a trans-conductance of 20mS

Figure 5.4: Graphic User Interface for Measurement with LABVIEW


to keep the in-band filter response independent of the magnitude of the out-of-band interferers.

In Figure 5.5, the OTA in the TIA is measured to be in class-A with small input current. A 5dB

gain peaking occurs due to the finite trans-conductance “Notch effect” studied in early chapters

and finite GBP of the op-amp after 30MHz where the zeros should produce a flat response as in

the theoretical plot Figure 3.5. The peaking reduces the selectivity of the filter but can be

improved by increasing the input ground capacitance, which further enhances the stability since

the phase margin is maintained above 30 degrees from all corner simulations in Chapter 4. When

the transfer function is measured with a large input signal beyond the zeros location, an adaptive

transfer function is realized shown in Figure 5.6 for the lowest cut-off frequency configuration.

The OTA starts to work in class-AB stage with large input-signals (i.e. above 1 mA) to push the

zeros at higher frequency with a larger trans-conductance. The selectivity is automatically

improved up to 13dB and the gain peaking effect is disappeared. Notice that with higher

bandwidths, the zeros are already pushed at high frequency and the finite GBP of the op-amp is

not changed much, thus producing more complex poles with lower gain peaking at higher

frequency and the effect is also mitigated by the presence of the input ground capacitances.

Figure 5.5: Measured Transfer Function of the Reconfigurable TIA

1M 10M 100M

Frequency (Hz)

Gai

n (

dB

Ω)

80

60

40

70

50

30

20

5dB


5.2.2 Input Impedance

Figure 5.6: Measured Adaptive Transfer Function of the TIA (Lowest Bandwidth)

1M 10M 100M

Frequency (Hz)

40 µA

1.8 mA

2.4 mA

3.2 mA

80

60

40

70

50

30

20

10

13dB

Gai

n (

dB

Ω)

Figure 5.7: Measured Input Impedance of the Reconfigurable TIA

1M 10M 100MFrequency (Hz)

Input

Imped

ance

(dB

Ω)

55

45

35

50

40

30

25

60

65


The input impedance measurement shown in Figure 5.7 is done by measuring the input voltage

swing divided by the small input current (i.e. 40uA). An adaptive input impedance characteristic

is also realized due to the class-AB stage OTA. The measured fully differential input impedance

is able to reach lower than 150Ω (in Figure 5.8) after one octave of the cut-off frequency (i.e.

5.6MHz) to ensure a limited voltage swing even in presence of large interferers (a few mA). To

have comparable input impedance and cut-off frequency, the filtering TIAs in Chapter 3 would

have required a very large differential input capacitance greater than 200pF which is almost 4

times more than the total input capacitances used in this design.

5.2.3 Two-Tone Intermodulation Test

The two-tone intermodulation test is done by placing one tone at 10MHz, and by moving down

the other tone from 20MHz in order to sweep the IM3 product the entire filter pass-band (as done

in [6]). Figure 5.9 shows the output IM3 product with high-pass shaping within the filter pass-

band due to the filtering effect provided by the input capacitance C1. The measured IIP3 for

Figure 5.8: Measured Adaptive Input Impedance in Ohms (Lowest Bandwidth)

1M 10M 100MFrequency (Hz)

Input

Imped

ance

(Ω

)250

150

50

200

100

0

300

100K

40 µA

1.8 mA

2.4 mA

3.2 mA


lowest bandwidth is 48.5dBm by placing the tones at 10MHz and 19.5MHz, and 36.1dBm for

the highest bandwidth by placing the tones at 50MHz and 95MHz.

Another IM3 measurement is done by placing two tones at 40MHz and 79MHz respectively to

show that the filter with large input signal at higher frequency, especially at the gain peaking

frequency 40MHz, the IM3 product at 1MHz tends to bend to achieve a higher linearity but the

filter is not compressing. In order to feed in with a large input current signal (some mA), the

input resistor for voltage to current conversion used is 500Ω single ended, thus 1kΩ for fully

differential structure. Figure 5.10 below shows that as the input power increases up to 20dBm,

which is approximately 3.2mA in amplitude, the IM3 product started to bend beyond 16dBm

which is about 2mA in amplitude. While in Figure 5.11, the first tone is placed in-band at 1MHz

with a small input level to ensure that the output does not saturate, and sweeping the second tone

amplitude which is placed out-of-band at 40MHz same as in Figure 5.10. It clearly shows that

the filter 1dB compression point is with input current greater than 5mA while the in-band gain

remains constant and out-of-band filtering improves up to 13dB as in the filter adaptive transfer

function. Therefore, the IIP3 for large signal input below 5mA is automatically improved when

the OTA is working in class-AB.

Figure 5.9: Two Tone Tests: Output IM3 In-band High-pass Shaping (Lowest bandwidth)

-50

-60

-70

-55

-65

-75

-80

-45

-40

0.01 0.1 1

ωIM3/ ωcut-off

IM3 (

dB

M)


Figure 5.10: IM3 Product Bends for Large Input Signal

1 dB/dB

3 dB/dB

20

-20

0

-40

-608 10 12 14 16 18 20

Pow

er (

dB

m)

PIN(dBm)

Figure 5.11: 1-dB Compressing Point with Large Out-of-Band Input Signal

60

50

40

55

45

35

30

65

70

75

80

0.5 0.8 1 3 5

Gain @40MHz

Gain @1MHz

Gai

n (

dB

Ω)

Input Current Signal Amplitude at 40MHz (mA)


5.2.4 Noise Measurement

Since the noise floor of the filter is lower than the differential probe itself, the small PCB is built

with an instrumentation Op-Amp to amplify the noise signal in order to measure the output noise

spectrum. The Op-Amp closed-loop gain is chosen to be 5, which is 14dB to measure the output

noise. Figure 5.12 and Figure 5.13 are the output noise spectrum measured at the output of the

instrumentation op-amp on the small PCB for the lowest bandwidth and highest bandwidth

configuration, respectively. It can be clearly seen that the flicker noise dominates at low

frequency; a flat in-band noise shaping for the lowest bandwidth; and a high-pass shaped in-band

noise for the highest bandwidth as in the simulation. The peaks in the noise spectrum come from

the random noise on the PCB due to insufficient de-coupling capacitors for the power supply,

and current biases. These peaks do not contribute significantly to the total integrated noise and

got averaged when doing the calculation. The output integrated noise is calculated and divided

by the total gain of the filter and the instrumentation op-amp thus it is reported as the integrated

input referred noise of 18.4μVRMS and 33.1μVRMS over the channel bandwidth of 1.92MHz

(WCDMA) and 10MHz (LTE20), respectively.

Figure 5.12: Measured Output Noise Spectrum for Lowest Bandwidth

1M100K10K

-144

-145

-146

-147

-148

-149

-150

Frequency (Hz)

No

ise

Sp

ectr

um

(dB

V2/H

z)

-143

-142

-141


5.2.5 Performance Summary and Comparison

The TIA prototype performance and measurement results are presented in Table 5.1. The

prototype is implemented in IBM 0.13μm CMOS process, runs with 1.2V supply. The total

current consumption of the prototype is 1.6mA for all the bandwidth configurations, leading to a

total power consumption of 1.92mW. The active die area is 0.45mm2, dominated by the MIM

capacitors. The total capacitance used is 104pF and 51pF for the lowest and largest bandwidth

configuration respectively. The bandwidth tuning range is achieved between 2.8MHz and

12MHz. The input impedance is maintained below 150Ω for the lowest bandwidth above one

octave from the filter cut-off frequency. The FOM calculated using equation (4.7) varies between

176dB(J-1

) and 182dB(J-1

). The table of comparison with other published works is shown in

Table 5.2. This work shows the best FOM among all these state-of-the-art filters, although the

area is not the best one.

Figure 5.13: Measured Output Noise Spectrum for Highest Bandwidth

10M100K10K 1M

-130

-135

-140

-145

-150

-155

No

ise

Sp

ectr

um

(dB

V2/H

z)

Frequency (Hz)


Table 5.1: Summary of Measurement Results

Circuit Parameters


R2 (kΩ) 5.86 2.93 1.95 1.465 1.172 0.977

C1 (pF) 14 10.5 11.5 10.5 11.5 9.5

C2 (pF) 6 6 6 6 6 6

αC2(pF) 6 4 2.5 2 1.5 1.5

Cs Fully Differential (pF) 28 12 12 6 4 2


Differential (pF) 104 85 69 59 57 51

Trans-conductance

gm (mS) (400μA

Bias Current)

20 20 20 20 20 20

Measured Results


(MHz) (Figure 4.15)

2.8 4.9 6.7 8.3 9.8 12

DC Power (mW) 1.92 1.92 1.92 1.92 1.92 1.92

Number of Poles 2 2 2 2 2 2

Maximum Differential

Input Impedance (dBΩ)

(Figure 4.17)

48.5 52.6 54.5 56.6 58 60

IIP3 out-of-band (dBm)

(Figure 4.20, Figure 4.21)

48.5 n/a n/a n/a n/a 36.1

Input Referred Noise

Integrated over 1.92MHz,

and 10MHz (µVRMS)

(Figure 4.19)

18.4 n/a n/a n/a n/a 33.1

SFDR out-of-band (dB) 86.8 n/a n/a n/a n/a 75.1

FOM dB(J-1

) 182 n/a n/a n/a n/a 176.1


Table 5.2: Comparison with other published works

This

work

[6]

JSSC10

[7]

JSSC06

[8]

JSSC02

[9]

JSSC07

[10]

JSSC05

[11]

JSSC07

[12]

JSSC09

Technology (nm) 130 90 130 800 180 250 130 180

Voltage Supply [V] 1.2 2.5 1.2 2.7 1.8 2.5 1.2 1.2

DC Power [mW] 1.92 1.26 3.4 6.21 4.86 7.3 1.8 4.7

Cut-Freq [MHz] 2.8 2.8 2.11 1.92 2 2.2 2.75 2

Number of Poles 2 4 4 5 5 3 5 3

IIP3 out of band

[dBm] 48.5 35.6 31 41 33 15 24 17.3

Input Referred

Noise[µVRMS] 18.4 32 36 47 80 52 116 181

SFDR out of band

[dB] 86.8 75 71.25 76.5 68 58.5 59.75 52

Area (mm^2) 0.45 0.50 0.90 2.86 0.38 0.50 0.57 0.23

FOM [dB(J-1)] 182 174 165 168 161 148 159 143

This

work

[13]

JSSC09

[14]

JSSC15

[15]

JSSC06

[16]

JSSC06

[17]

JSSC09

[18]

JSSC09

[19]

JSSC11

Technology (nm) 130 130 180 130 180 130 130 180

Voltage Supply [V] 1.2 0.55 1.8 1.2 1.8 0.6 1.0 1.5

DC Power [mW] 1.92 3.5 1.38 14.2 4.1 3.5 7.5 4.35

Cut-Freq [MHz] 12 11.3 33 11 10 11.3 20 13.5

Number of Poles 2 4 4 4 4 4 5 6

IIP3 out of band

[dBm] 36.1 13 18 21 7.5 10 26 22

Input Referred

Noise[µVRMS] 33.1 110 45 36 23.7 110 232 355

SFDR out of band

[dB] 75.1 53 61.3 64.6 58.0 50.8 57.1 52.0

Area (mm^2) 0.45 n/a 0.14 0.9 0.43 0.52 1.53 1

FOM [dB(J-1)] 176.1 154 171.1 159.5 157.9 151.9 158.4 154.7

CHAPTER 6. CONCLUSION 78

Chapter 6

Conclusion

6.1 Summary

This thesis focused on the down-converted signals from current passive mixers in wireless

receivers. Noise, distortion and losses are strictly correlated to the stage following the mixer

called trans-impedance amplifier. A robust TIA solution is developed and compared with other

state-of-the-art continuous time filters in terms of bandwidth re-configurability, input impedance,

noise, linearity, power and area to address the wireless applications. The filter structure is studied

theoretically and compared with other two common TIAs in detail, with a high-pass shaping of

noise and distortion due to the input capacitance connected with the active feedback network.

The circuit transistor level implementation is shown and the simulation results are presented in

Chapter 4. The TIA prototype was fabricated in IBM 0.13μm CMOS process with a die area of

0.45mm2. The power consumption of the prototype is 1.92mW with a 1.2V supply. The

bandwidth re-configurability of the filter is done by tuning the capacitor banks through digital

controls with a National Instruments FPGA. The measured tuning range is between 2.8MHz and

12MHz, achieved a SFDR varies between 86.8dB and 75.1dB with a FOM varies between

182dB(J-1

) and 176dB(J-1

) for the lowest bandwidth and largest bandwidth respectively.

6.2 Future Work

The filtering TIA in this thesis showed a good performance and it is suitable for the current

passive mixers in terms of input impedance, noise and linearity. However, this is only a small

building block of the entire wireless receiver chain. It could not be tested with an actual current

mixer. Therefore, to expand the scope of this thesis, further work is required to realize a

complete functional receiver with this TIA topology, and how it improves the overall

performance in the receiver chain.

CHAPTER 6. CONCLUSION 79

The biasing of the class-AB OTA requires doubled capacitance in the feedback network, further

work would involve finding another biasing technique to reduce the use of extra capacitance,

such as a floating battery [20],[21].

The linearity and FOM drops with larger bandwidth due to finite op-amp GBP. The op-amp

requires further work to have the GBP tuned for all bandwidths configuration without

compromising the selectivity of the filter.

BIBLIOGRAPHY 80

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ADAPTIVELY FILTERING TRANS-IMPEDANCE AMPLIFIER FOR RF … · 2016-06-21 · ii Abstract Adaptively...

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