### Implementation in SimRF

```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
1
Outline
1. Goal
2. Two types of a matching circuit
3. Two basic op-amp configurations
4. Comparing two noisy circuits
5. Noise analysis and comparison-Theory and SimRF
6. RF low-frequency power detector – circuit schematic
7. RF low-frequency power detector – switching capacitors
8. RF low-frequency power detector – coil configuration
9. RF low-frequency power detector – Ultiboard setup/photo
10. Demo
11. Future work
2
Our goal
• Compare two different noisy
circuits in SimRF
• RF power meter
• Low frequency wideband
communications
3
Two types of matching circuit
At the resonant
frequency:
VT  Vemf  Vo 90
ZT  R
VT  QVo 0
ZT  Q 2 R
where Q  L
R
4
Two basic op-amp configurations
Inverting configuration :
S (t )  0
Non- inverting conf.:
S (t )  0
 R  RS
eNi2  eR21   1
 R2
2
2
2
 2  R1  RS  R2  2
 eR 2  
 eN  ( R1  RS ) 2 iN2
R2



2
2
 R2  2  R1  2
 R1 R2  2
2 2
2
2






eNi  
e

e

e

i

R
S iN
 R1  R  R  R 2 N  R  R  N
R

R
2 
2 
2 
 1
 1
 1
5
Comparing two noisy circuits
(1) series/inverting
In our circuit:
R  40, L  2.16mH, B  20kHz
For a resonant frequency
f o  200kHz :
C  293pF
Inverting amplifier
gain:
R2
G
R1  RT
Total circuit gain:
G  G
R1  0
R2  5.428k
G  135.7
 G  135.7
6
Comparing two noisy circuits
(2) parallel/non-inverting
In our circuit:
R  40, L  2.16mH, B  20kHz
For a resonant frequency f  200kHz :
C  293pF and Q  67.9
o
Non-inverting
amplifier gain:
R
G  1 2
R1
Total circuit gain:
G  Q  G
R1  1k
R2  1k
G2
 G  135.7
7
Noise Analysis-Theory
Series/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 :
eR  4kTBR  1.138107
eRout  G 4kTBR  1.544105
2
eNi  3.911012
eout  eRT out  (G  eNi ) 2  (1.544105 ) 2  (2.6831104 ) 2  0.269m V
2
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:
eR  4kTBR  1.138107
eRout  G 4kTBR  1.544105
eNi  2.170109
2
eout  eRT out  (G  eNi ) 2  (1.544105 ) 2  (9.316105 ) 2  94.4V
2
8
Reminder: MATLAB script for finding the
noise figure using the previous analysis:
clear all;
k
= 1.38066e-23;
T
= 298;
VT
= 4*k*T;
B
= 2e4;
%
%
%
%
Boltzmann constant [J/K]
temperature [K]
temperature constant [W/Hz]
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
9
SimRF set-up and results
Series/Inverting
Parallel/Non-Inverting
10
Comparison with theory
Series/Inverting:
The calculated rms output voltage (Theory) was:
eNout  269V
eNout  267V
The output from the experimental setup was a close match:
Error 
269  267
100 %  0.74%
269
Parallel/Non-Inverting:
The calculated rms output voltage (Theory) was:
eNout  94.4V
The output from the experimental setup was a close match:
Error 
eNout  93.1V
94.4  93.1
100 %  1.38%
94.4
*The experimental setup calculates a running rms so this could be a source of error.
11
Circuit Schematic (RF power meter)
12
Switching Capacitor Bank
13
Coil Configuration
14
Ultiboard Setup
15
Future Work
1. 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.
16
```