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I am trying to calculate bode plot of a circuit.

For proteus my frequency at -63dB is 18 kHz as sample the circuit connection and its bode plot is provided.

proteus code enter image description here

Using analytical approach I calculate the transfer function as enter image description here and its bode plot using matlab code is calculate using

R2=976; R1=(998e3); R3=22; C=8200e-12; num=([R2]); den=([2*C*R3*R1+2*C*R3*R2 (R1+R2)]); G=tf(num,den); options = bodeoptions; options.FreqUnits = 'Hz'; % or 'rad/second', 'rpm', etc. figure(1) bode(G,options); grid on

The frequency for -63dB is 441 kHz.

Where am I making mistake please identify it?

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    \$\begingroup\$ Already the 1st line in your calculation is wrong. The first voltage divider is - of course - loaded by the succeeding sections. \$\endgroup\$ Commented Aug 21, 2024 at 14:49

3 Answers 3

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Your are over complicating things by jumping into the math before simplifying things. For example consider what I have done below (shorted out the input signal): -

enter image description here

I've shorted it out because the circuit still has the same inherent RC time constant when the input is at 0 volts. From this, you can see that you can largely ignore R1A and R1B because they (together) are a thousand times the resistance of R2.

That leaves you with this: -

enter image description here

This means that the 8.2 nF capacitor is in parallel with 1020 Ω so, if you calculate RC on that basis you will arrive at around 19 kHz.

This is what an EE would do. What you did was attempt a mathematical route without simplifying the basic structure (never a good plan).

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I solve the question using Nodal analysis and now my answer is correct. enter image description here Further these equations were solved by Matlab using minor-expansion

R3 = 22; C = 8300e-12; R2 = 976; R1 = 998000; syms s Vin A = [-(1/R3), -C*s, (1/R3)+C*s; (1/R3) + (1/R2) + (1/R1), 0, -1/R3; 0, (1/R3)+C*s, -C*s]; X = [-(1/R3), -C*s, 0; (1/R3) + (1/R2) + (1/R1), 0, Vin/R1; 0, (1/R3)+C*s, 0]; %B = det(A); B = det(A,'Algorithm','minor-expansion') Y = det(X,'Algorithm','minor-expansion') L = 47228722131631622161554866441955/2635146649435747461060372959951613029515264; %B[1] M = 406459372473413/191817315328964165632; %B{2} den = [L M]; N = 55187463665407821/145987464125023389879168401408000;%Y[1] O = 302231454903657293676544/145987464125023389879168401408000; %Y[2] num = [N O]; G = tf(num,den); options = bodeoptions; options.FreqUnits = 'Hz'; figure(1) bode(G,options); xlim([10 100000000]) grid on

Everyone thanks for the help

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Simplify the problem by combining the obvious (the two 499k resistors). You can make a Thevenin equivalent as you tried to do, but not completely which left you with a mess.

schematic

simulate this circuit – Schematic created using CircuitLab

Write your equation for the simplified version and graph. You'll get somewhere around 18 kHz at -63 dB. Be sure you convert the complex number in to magnitude (I'm not familiar with Matlab syntax, but I'm assuming that the bode option will give magnitude).

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