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Prof. Joo Vaz

Wireless Integrated Circuits and Systems Group

Instituto de Telecomunicaes

Instituto Superior Tcnico

Technical University of Lisbon

MONOLITHIC INTEGRATED

MIXERS

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MixerCircuit whose function is the frequency translation

of a given signal.

Working behaviorTo perform the frequency translation a nonlinear ora time variant behavior must exits.

Only a circuit like this will produce new frequencies

at the output that do not exist at its inputs.

If the required translation is to a multiple frequency

of the input, it is only necessary to use one of the

output signal harmonics.

Introduction

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However if the required frequency is not harmonicallyrelated with the input, an auxiliary oscillator must be

used (local oscillator LO) to perform the translation.

Transceiver applicationIn the emitter (up-conversion): frequency translationfrom a baseband (BB) or low frequency signal IF1(intermediate frequency - IF) to a higher frequency

signal, like transmission frequency (RF) or IF2.

In the receiver (down-conversion): frequency

translation from RF or IF1 to a lower frequency signal,IF2 or BB.

Introduction

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mixers

switched non switched

diodes on/offtransistors on/off forward bias diodesactive region transistors

Classification

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Conversion gainPower (or voltage, current, etc) gain between input andoutput signals. Receiver example:

GC=PIF/PRF or GC=vIF/vRF.

The power gain can be transducer, available or power gains.

Ports matchingSome of the mixer ports, RF, LO or IF, can be matched to a

certain impedance value. In this case their matching is

usually characterized with reflection coefficient.

MISTRF

OL

FI

Characterization

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Conversion gain compressionLike in an amplifier, 1dB compression point for theconversion gain can be obtained. It is desirable that the

mixer does not reach that point in order to avoid the output

signal amplitude distortion. In systems with phase

modulated signal GC phase distortion must be analyzed

also.

Conversion efficiencyRatio between the mixer output power (PIF) and the total

power (AC+DC) supplied to the mixer (PRF +PLO +PDC).

LO powerRequired local oscillator power, PLO, at LO port. The higher

its value, harder to design LO will be.

Characterization

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Noise factorRatio between the input SNR (at input frequency) to theoutput SNR (at output frequency).

Receiver example:NF=SNRRF/SNRIF.

LO-IF isolationIs the LO attenuation when it reaches the IF port. Thisvalue must be as high as possible.

LO-RF isolationIs the LO attenuation when it reaches the RF port. Thisvalue must be as high as possible.

Characterization

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One-tone excitation

NLv

i

vOL

VDC

Assuming that the nonlinearity is i=f(v) type and memoryless (withoutreactive elements) an analytical analysis can be easily made.

Assuming that v is applied.

Example: NL is a PN junction

( )S DC lo LO T

vi I exp v V V cos t

nV

= +

( )

( ) ( ) ( ) ( )

DC lo LO

S

T

lo LO DC DC S S 0 LO n LO LO

n 1T T T

V V cos t i I exp

nV

V cos t V Vi I exp exp I exp I x 2 I x cos n t

nV nV nV

+

=

+= =

= = +

where the n-order modified Bessel functions In(x) were used and

lo

LOT

Vx

nV=

Analysis

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The current is ( ) ( )0 1 LO 2 LO i I I cos t I cos 2 t = + + +

where

( ) ( ) ( )DC DC DC 0 0 LO S 1 S 1 LO 2 S 2 LO T T T

V V VI I x I exp I 2I exp I x I 2I exp I x

nV nV nV

= = =

DCcomponent 1

st harmonic 2nd harmonic

Note:All the components depend on VDC and VLO.

Analysis

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Two-tone excitation

NLv

i

vOL

VDC

vRF

Assuming that both signals can produce harmonics, i.e., they are notsmall signals.

( ) ( )S DC lo LO rf RF T

v

i I exp v V V cos t V cos t nV

= + +

( ) ( )

( ) ( )

( ) ( ) ( ) ( ) ( ) ( )

DC lo LO rf RF

S

T

lo LO rf RF DC

S

T T T

DCS 0 LO n LO LO 0 RF n RF RF

n 1 n 1 T

V V cos t V cos t i I exp

nV

V cos t V cos t V

I exp exp exp nV nV nV

VI exp I x 2 I x cos n t I x 2 I x cos n t

nV

+ +

= =

+ +=

=

= + +

rf

RFT

Vx

nV

=

where

Example 1:Both signals are large

Analysis

lo

LOT

Vx

nV=

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Now, assuming that one of the signals is weak and can be considerera small signal. An equation for the current i can written using Taylor

series up to 1st order:

( ) ( ) ( )strong

strong weak

strong weak V

i f v d f vi f V v v V v d v

= + = +

strong DC LO weak RF v V v v v = + =

( )( )

( ) ( )

strong

lo LO DC lo DC strong S S

T T T

lo LO S DC lo S DC

T T T T T V

V cos t V v Vf V I exp I exp exp

nV nV nV

d f v V cos t I V v I V exp exp exp

d v nV nV nV nV nV

+= =

+

= =

Example 2:One of the signals is small

Analysis

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Using Bessel functions:

( ) ( ) ( ) ( )

( )( ) ( ) ( )

strong

DCstrong S 0 LO n LO LO

n 1T

S DC0 LO n LO LO

n 1T TV

Vf V I exp I x 2 I x cos n t

nV

d f v I Vexp I x 2 I x cos n t

d v nV nV

+

=

+

=

= +

= +

( ) ( ) ( )

( ) ( ) ( ) ( )

DCS 0 LO n LO LO

n 1T

S DC0 LO n LO LO rf RF

n 1T T

Vi I exp I x 2 I x cos n t

nV

I Vexp I x 2 I x cos n t V cos t

nV nV

+

=

+

=

+ +

+ +

wRF, wLO wRF, 2wLO wRF, 3wLO wRF, terms only

DC, wLO

, 2wLO

, 3wLO

, terms only

Analysis

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Single-balanced mixer

v1

VDD

RD

M1

M2

RD

iSS

vout

Uses a differential pair. Its easy to show that,

2 2

2 2SS SS SS SS

D1 1 1 D 2 1 1

i K i i K i K Ki v v i v v

2 2 4 2 2 4

= + =

!2

2SS

out D 1 1

K i Kv 2 R v v

2 4

=

If v1 is one of the input signals and iSS is related with the other, the

nonlinear relation will do the mixing. Some simplification can beapplied:

2 SS

SS 1 out D 1

K iKi v v 2 R v

2 2

>> =

Note that if iSS is DC

m1out D 1 v 1

gv 2 R v A v

2= =

= dif. pair in linear regime

Circuits

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v2

M3

iSS

Usually iSS

is obtained with a MOSFET:

( )2

SS 3 2 T 3 i K v V =

Comments:

2 quadrants multiplier because v2>VT3. Bad LO-IF isolation. Good LO-RF isolation. vRF input is single-ended, vIF output is differential. Moderate GC, low NF, low PC(-1dB).

!

3 D

C ol

K K RG V2

=

( )out 3 D 1 2 T 3 v 2 K K R v v V =

v1=vLO, v2=vRF and vout=vIF leads to !

Circuits

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If v1=vLO has enough amplitude, M1 and M2 transistors will behaveas switches.

Assuming that iSS=ISS+Irfcos(wRFt)

vOL

VDD

RD

RD

iSS

vout

( ) ( ){ }

( ) ( ){ }

D1 SS rf RF LO

D 2 SS rf RF LO

1i I I cos t 1 sgn cos t

21

i I I cos t 1 sgn cos t 2

= + +

= +

( )D1 DD D1 out D1 D 2 D 2 D1 D 2 DD D 2

v V R i v v v R i i

v V R i

= = =

=

!

( ) ( )out SS rf RF LO v R I I cos t sgn cos t = +

Switching behavior

Circuits

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Additional comments

Transistors have to switch fast. High LO amplitude required.

If current iSS is obtained from vRF with MOS transistor (M3), if vRF isa small signal

out m 3 rf c m3

2 2V R g V G R g

= =

Note: This eq.

was used( ) ( ) ( )LO LO LO

4 4sgn cos t cos t cos 3 t

3 = +

Circuits

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v2

VDD

RD

M3

M4

RDv

out

M5

M6

v1

M1

M2

ISS

Assuming that all transistors are equal:

2

2D1 D1

D 3 2 2

2

2D1 D1 D 4 2 2

2

2D 2 D 2

D 5 2 2

2

2D 2 D 2

D 6 2 2

i K i Ki v v

2 2 4

i K i Ki v v2 2 4

i K i K i v v

2 2 4

i K i K i v v

2 2 4

= +

=

=

= +

( ) ( )2 2

2 2D1D 2

out DD D D 3 D 5 DD D D 4 D 6 2 D 2 2

K iK i K K v V R i i V R i i 2v R v v

2 4 2 4

= + + =

For the output voltage

Double-balanced mixer (Gilbert cell)Circuits

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Currents iD1 and iD2 are given by:

2 2

2 2SS SS SS SS

D1 1 1 D 2 1 1

I K I I K I K Ki v v i v v

2 2 4 2 2 4

= + =

With the previous equations vout=f(v1,v2) can be obtained, howeverfunction f is analytical complicated. So, in order to obtain a

multiplication some approximations will be made.

- M1 and M2 differential pair is working in linear region

SS SS SS SS

D1 1 D 2 1

I K I I K I i v i v

2 2 2 2

+

2 2

2 2SS SS SS SS

out 2 D 1 2 1 2

K I K I K I K I K K K K v 2v R v v v v

4 2 2 4 4 2 2 4

= +

!

Circuits

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- Second onder terms v22 are negleted

SS SS SS SS

out 2 D 1 1

K I K I K I K I K Kv 2v R v v

4 2 2 4 2 2

= +

!

Using the approximation valid for x

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Comments

4 quadrants multiplier. Good isolation between OL, RF e FI. High GC, low NF. Linearity is higher than the single-balanced case. Differential inputs and output.

Circuits

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Micromixer

vOL

VDD

RD

M4

M5

RDv

out

M6

M7

vRF

ISS

M3

M2

M1

vGG

Based on Gilbert bipolar mixer[IEEE JSS, Sept. 1997].

Better IP3 due to 3rd-order mixingproducts cancelation.

Easy matching at RF input. Single-ended RF input. Low dynamic range.

Circuits

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Substrate mixer

v2

VDD

RD

M1 M2

RDv

out

v1

M3 M4

The idea is to use the substrateas a second gate. This solution

is common wi th d iscre tetransistors.

Requires a triple-well technology,i.e., a p-well inside a deep n-well.

Circuits

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Potentiometric mixer

M1

M2

M3

M4

vOL+

vOL-

vRF-

vRF+

vRF+

vFI

Transistors work on triode regionas variable resistances.

Reactive components filterunwanted high order mixing

products.

Highly linear but high NF. OPAMP can be a low frequency

component.

Circuits

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Switching passive mixer

M3

M4

vFI

M1

M2

vOL+

vOL+

vOL-

vOL-

vRF+

vRF-

Low conversion gain. High linearity. Mi switching High level LO.

Circuits

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Time domain simulation is the transient simulation made bysimulators like Spice.

For strongly nonlinear circuits where frequency excitations are non-

correlated it is the best choice.

Usually simulation time is very long in circuits that have time

constants with large differences like high frequency circuits.

To solve this problem, for example, simulator Spectre uses theperiodic steady-state analysis (PSS). The simulation is performed in

the time domain but the method, after a initial brief transient

simulation, tries to find the steady-state solution by an iterativeapproach.

Simulation

Time-domain simulation

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Harmonic-balance simulation method is one example of time-frequency simulation.

ADS from Agilent or Microwave Office from AWR implement it.

The linear part of the circuit is analyzed in the frequency-domain and

the nonlinear part in the time domain. Fast Fourier transform (FFT) is

used in the method interactions.

The simulation only analyses the steady-state regime.

Simulation

Time-frequency domain simulation

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The mixer simulation can be made in different ways. It dependson what behavior is desired.

With this non-linear and/or time-variant circuit the time domain

simulation can always be used. The results are voltages and

currents in the time domain and, if quantities in the frequencydomain are required, tedious post-procession FFT is necessary.

However, Cadence environment has other kind of simulations

where frequency domain quantities are easily obtained.

PSS simulation can be used when all signals create non-linear

behavior. Still, if only one signal creates that behavior, a small-

signal large-signal analysis can be done. PSP, PAC and PNOISE

are examples of that and they must be performed in conjunction

with PSS.

Simulation

Mixers simulation with Cadence

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A Gilbert cell mixer for fRF=3.5GHz, fLO=3.4GHz and Itail=4mA ispresented.

Mixer core

Simulation

Simulation examples

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Time domain simulation

Simulation

It was assumed that RF source and IF load have 1kimpedances. The LO source has low output impedance.

Test cell example

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Simulation

Simulation results (differential RFin, LO and IF voltages)

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PSS simulation

The mixer has four signal sources: 2 at fRF and 2 at fLO. Thebeat frequency is automatically chosen to 100MHz. Like this

any intermodulation product can be selected.

pss form example

Simulation

Test cell example(equal to time domain)

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Results can be viewed taking into account the intermodulation

frequency values between fRF and fLO.

Simulation

Direct plotform for GPC

Direct plotform for YLO

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Simulation

Isolation can be obtained using the power gain result between LO

and RF/IF ports. From YRF and YLO input admittances equivalents

parallel Cp//Rp are calculated.

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PSS and PSP simulation

Simulation

Test cell example psp form example

PSS simulates LO unique large-signal source. Then PSP makes a

small-signal simulation for RF and calculates all the mixing

products with LO.

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PSIN ports are used to identify

s-parameter ports like in the SPanalysis.

A LO harmonic is associated to

each port. The band for each

port is the mixing product

between input frequency bandand port harmonic.

Simulation

Direct plot form for PSP

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Simulation

GT & GP Noise figureInput & output

matching

Some PSP results are presented. Please note that results are always

referenced to input frequency band, although some of them belong to

other bands.

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DECT double-conversion mixer with AMS CMOS 0.6mm technology(fRF=1.9GHz, fIF=10MHz) (F. Azevedo and M J. Rosrio, 2002)

Occupied area:

With pads = 0.64mm2

Without pads = 0.1mm2

0.8mm

0.8mm

Layout

The mixer has two stagesand requires two LO:

fLO1=1.7GHz, fLO2=190MHz.

Differential RF input,quadrature differential IF

outputs.

Quadrature differentialLO1 and LO2 inputs.

Examples

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Test-bench system diagram

VLO1i+

VLO1i-

VLO1q-

VLO1q+

VLO2i+

VLO2i-

VL

O2q-

VL

O2q+

VRF+

VRF -

VBBi+

VBBi-

VBBq-

VBBq+

VRF

VLO1

VLO2

Conv. SingDif. de RF

Conv. SingDif.

+

Circ. Polifsico de LO2

Conv. SingDif.

+

Circ.Polifsico de LO1

C.I. Misturador+

-

vRF(t)

+

-

vLO1 (t)

+

-

vLO2 (t)

Examples

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Test board (IC is chip-on-board (CoB) mounted)

Single-Ended todifferential RF input

(1,9GHz)

Single-Ended todifferential LO1

input (1,7GHz)

Single-Ended-Diferencialde LO2

(190MHz)

IC mixer

45mm

55mm

Examples

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Complete test-board

Examples

MT 2012/2013Examples

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Experimental results

-25

-15

-5

5

15

25

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

PRFc [dBm]

PBBi

[dBm]

-5

0

5

10

15

20

Gc[dB]

P BB iExperimental

P B B iS imulado

G cE xperimentalGcSimulado

Conversion gain and BB output power

Conditions:

PRF variable@1880,1MHz;

POL1 = POL2 = +7dBm,

fLO1= 1700(1690)MHz,

fLO2 = 190MHz;

VDD = 3,3V.

Examples

MT 2012/2013Bibliography

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Razavi, B., RF Microelectronics, Prentice Hall, Inc., 1998.

Lee, T., The Design of CMOS Radio-Frequency Integrated Circuits,

Cambridge University Press, 1998.

Crols, J., Steyaert, M., CMOS Wireless Transceiver Design, Kluwer

Academic Publishers, 1997.

Maas, S., Microwave Mixers, Artech House, Inc., 1993.

Maas, S., Nonlinear Microwave and RF Circuits, Artech House,

Inc., 2003.

Rosrio, M. J., Projecto Assistido por Computador de

Misturadores com TECMES para Microondas, PhD thesis, IST,

Maio 1992.

Bibliography