% This script simulates the first stage of a cascaded CE-CE BJT circuit.
% See Figure 11-30 of this document and the analysis that follows.
% A hybrid-pi small signal model is assumed.
% The resulting system is represented in state space form below.
A=[-1.068e6,224.883e3;-4.950e9,-11.019e6];
B=[68.027e6;3.305e9]
C=[1 -1]
D=[0]
eigs(A)
4./abs(real(eigs(A)))
del=cos(tan(imag(eigs(A))./real(eigs(A))))
wn=abs(eigs(A))
% The above data indicates the system has a BW of approx. 5.15MHz
% and a gain of 300. We can improve the circuit to get increased gain
% by using feedback at the expense of BW. The commands below are designed
% to reduce the BW to approx. 51.5KHz with a corresponding gain increase.
% The resulting circuit has a gain of approx. 3e6, an increase of x10,000.
rank(ctrb(A,B))
rank(obsv(A,C))
P=[-60435+j*3.299e5;-60435-j*3.299e5]
K=place(A,B,P)
eigs(A-B*K)
4./abs(real(eigs(A-B*K)))
del=cos(tan(imag(eigs(A-B*K))./real(eigs(A-B*K))))
wn=abs(eigs(A-B*K))
% The following commands generate the various plots.
figure
bode(A,B,C,D)
title('Bode Plot of Hybrid-Pi BJT Model')
figure
step(A,B,C,D)
title('Step Response of Hybrid-Pi BJT Model')
figure
bode(A-B*K,B,C,D)
title('Improved Bode Plot of Hybrid-Pi BJT Model')
figure
step(A-B*K,B,C,D)
title('Improved Step Response of Hybrid-Pi BJT Model')