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Noise Performance of Inverting and Non-inverting Amplifier Circuits -Implementation

in MATLAB SimRF

Application Note

Sheila P. Werth, Natasa Trkulja, Ali Magzari, Stephen J. Bitar & Sergey N. Makarov

ECE Dept. WPI, Worcester, MA

August 24th 2011

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Outline1. Goal2. Two types of a matching circuit3. Two basic op-amp configurations4. Comparing two noisy circuits5. Noise analysis and comparison-Theory and SimRF 6. RF low-frequency power detector – circuit schematic7. RF low-frequency power detector – switching capacitors8. RF low-frequency power detector – coil configuration9. RF low-frequency power detector – Ultiboard setup/photo10. Demo11. Future work

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Our goal

• Compare two different noisy circuits in SimRF

• RF power meter

• Low frequency wideband communications

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Two types of matching circuitAt the resonant frequency:

RZ

VVV

T

oemfT

90

RLQwhere

RQZ

QVV

T

oT

2

0

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Two basic op-amp configurations

Inverting configuration :

Non- inverting conf.:222

2

21

21222

2

21

121

2

21

22NSNNRRNi iRi

RRRRee

RRRe

RRRe

221

22

2

2122

2

2

121

2 )( NSNS

RS

RNi iRReR

RRReRRRee

0)( tS

0)( tS

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Comparing two noisy circuits (1) series/inverting

In our circuit:

For a resonant frequency

kHzBmHLR 20,16.2,40

:200kHzfo pFC 293

Inverting amplifier gain:

Total circuit gain:

TRRRG

1

2

GG

7.1357.135

428.50

2

1

GG

kRR

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Comparing two noisy circuits (2) parallel/non-inverting

In our circuit:

For a resonant frequency kHzBmHLR 20,16.2,40

:200kHzfo 9.67293 QandpFC

Non-inverting amplifier gain:

Total circuit gain:

1

21RRG

GQG

7.135211

2

1

GG

kRkR

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Noise Analysis-TheorySeries/Inverting:The noise generated by the antenna resistance is given by: After passing through the amplifier this becomes:The equivalent input noise to the amplifier is :The total predicted rms output noise is :

Parallel/Non-inverting:The noise generated by the antenna resistance is given by:Multiplying by the total circuit gain the noise that enters the amplifier due to the resistor is:The equivalent input noise to the amplifier is:

710138.14 kTBReR510544.14 kTBRGeRout

mVeGee NioutRout T269.0)106831.2()10544.1()( 242522

122 1091.3 Nie

710138.14 kTBReR

510544.14 kTBRGeRout92 10170.2 Nie

VeGee NioutRout T4.94)10316.9()10544.1()( 252522

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Reminder: MATLAB script for finding the noise figure using the previous analysis:

clear all; k = 1.38066e-23; % Boltzmann constant [J/K] T = 298; % temperature [K] VT = 4*k*T; % temperature constant [W/Hz] B = 2e4; % system (noise) bandwidth, Hz (cancels out) % Amplifier parameters en = 14e-9; % required (datasheet) in = 1.8e-12; % required (datasheet) RS = 1e3; % use an estimate when the exact value is not available R1 = 1e3; % required R2 = 100e3; % required Nin= k*T*RS*B; % reference input noise power (Pozar) % Inverting amplifier inv.eNi = sqrt(B)*sqrt( (R1+RS+R2)^2/R2^2*en^2 + (R1+RS)^2*in^2); inv.eR1 = sqrt(4*k*T*R1*B); % rms voltage noise inv.eR2 = sqrt(4*k*T*R2*B); % rms voltage noise inv.eR = sqrt(inv.eR1^2 + ((R1+RS)/R2)^2*inv.eR2^2); % inv inv.eNi = sqrt(inv.eNi^2 + inv.eR^2); inv.Na = inv.eNi^2; inv.NF = 10*log10(1 + inv.Na/Nin); inv % Non-inverting amplifier noninv.eNi = sqrt(B)*sqrt( en^2 + (R1*R2/(R1+R2))^2*in^2 +RS^2*in^2); noninv.eR1 = sqrt(4*k*T*R1*B); % rms voltage noise noninv.eR2 = sqrt(4*k*T*R2*B); % rms voltage noise noninv.eR = sqrt((R2/(R1+R2))^2*noninv.eR1^2 + (R1/(R1+R2))^2*noninv.eR2^2); % non-inv noninv.eNi = sqrt(noninv.eNi^2 + noninv.eR^2); noninv.Na = noninv.eNi^2; noninv.NF = 10*log10(1 + noninv.Na/Nin); noninv

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SimRF set-up and resultsSeries/Inverting

Parallel/Non-Inverting

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Comparison with theorySeries/Inverting:The calculated rms output voltage (Theory) was:

The output from the experimental setup was a close match:

Parallel/Non-Inverting:The calculated rms output voltage (Theory) was:

The output from the experimental setup was a close match:

VeNout 269

VeNout 267

*The experimental setup calculates a running rms so this could be a source of error.

VeNout 1.93

VeNout 4.94

%74.0%100269

267269

Error

%38.1%1004.94

1.934.94

Error

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Circuit Schematic (RF power meter)

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Switching Capacitor Bank

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Coil Configuration

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Ultiboard Setup

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Future Work1. Exclude the ground plane since it increases the

capacitance.

2. Use capacitors with no inductance to increase the frequency range.

3. Use different type of coils in order to improve circuit sensitivity.

4. Include the non-inverting amplifier before the peak detector.

5. Have a built-in screen indicating the resonant frequency.