E-4410 Electromagnetic and circuit simulations
Exercise 1.
7.1.2016
Do these at home
1.1
Solve the simultaneous equation
V12 + V22 − 1 = 0
V 2 − eV 1 = 0
to an accuracy of six decimal places using multivariable Newton-Raphson iteration. The
simultaneous equation has two solutions. Find both the solutions using suitable initial
guesses for V1 and V2 . Present the intermediate results of the iterations.
1.2
a. How do the MNA equations differ from those written for nodal analysis? Use the
impedance and the ideal voltage source as examples.
b. Write the MNA equation stamps (see the examples in the lecture slides) for the
impedance and the ideal voltage source.
Start doing these in class
Do an AC analysis on the given transistor amplifier circuit
using the AWRDE software.
RVc Vcc
Vc
Rb2
RL
out
1.3
Vin
Cb
Rin
in
Rb1
1
Q1
a. Make a Bode plot in the frequency range 1 Hz–1 GHz.
That is, plot |Vout | in decibels on the left y-axis, the
phase in degrees on the right y-axis, and use the logarithmic scale for the x-axis.
b. Find the operating point of all the elements in the
circuit.
Use the measurement element MProbe to measure voltage
Vout and the transistor model GBJT3 with the following parameters:
Is = 25 fA, βf = 120, VAF = 40 V, CJC = 20 pF, CJE = 20 pF.
Rb1 = 20 kΩ Rb2 = 180 kΩ RL = 1 kΩ Cb = 100 nF Vc = 10 V
RVc = 1 Ω
Vin = 1/0◦ V Rin = 1 Ω.
Do an AC analysis on the operational amplifier circuit using the AWRDE software, and plot the following three
graphs in their own windows (use the logarithmic scale for
the frequency):
C2
R3
1.4 in R1
C1
a. amplitude response in dB in the range 100 Hz–10 kHz,
out
O1
R2
b. the real and imaginary parts of the voltage Vout as a
function of frequency, and
c. the magnitude of the current through resistance R3
as a function of frequency.
d. Determine the bias voltage of all the nodes. Comment on your result.
e. Find the pass band half-power cut-off frequencies using the vertical and horizontal
marker drawing feature.
Use the operational amplifier model OPAMP by connecting the model’s node 4 to node 2
and connecting node 5 to ground with the following parameters:
M = 106 , R1 = R2 = 0 Ω, R4 = 100 kΩ, R3 = 10 Ω.
R1 = 1.1 kΩ R2 = 1.2 kΩ R3 = 150 kΩ C1 = 0.01 µF C2 = 0.01 µF.
RVc
Vcc
1.5
Vc
Rc
RL
out
Q2
Cb
Q1
in
Vs
Re
Ce
a. Plot the frequency response (use a logarithmic scale
for the frequency axis and dB for the voltage gain
axis) for the frequency range 1 Hz–100 MHz. Comment your simulation result.
b. At what amplitude of signal Vs is the amplitude of
the output voltage Vs 5 V? Use the tuner tool for
this.
Rf
Use the following BJT (simulator model GBJT3) parameters:
Is = 25 fA, βf = 110, VAF = 40 V, CJC = 20 pF, CJE = 20 pF.
Rc = 22 kΩ
RL = 2.2 kΩ Re = 470 Ω
Rf = 220 kΩ RVc = 1 Ω
Cb = 100 nF
Ce = 1 µF
Vc = 10 V
Vs = 1/0◦ V.
Return all your simulation files and answer documents by 14.1.2016, 12.15 pm to the appropriate
place under the AWRDE link in MyCourses.