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 G2 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 1.138107 eRout G 4kTBR 1.544105 2 eNi 3.911012 eout eRT out (G eNi ) 2 (1.544105 ) 2 (2.6831104 ) 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 1.138107 eRout G 4kTBR 1.544105 eNi 2.170109 2 eout eRT out (G eNi ) 2 (1.544105 ) 2 (9.316105 ) 2 94.4V 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 269V eNout 267V 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 94.4V The output from the experimental setup was a close match: Error eNout 93.1V 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