Monte Carlo AnalysisIn this study, you will perform a statistical analysis of an electronic circuit...

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Monte Carlo AnalysisIn this study, you will perform a statistical analysis of an electronic circuit under variations of different component parameters. You have to write a MATLAB program to perform...

Monte Carlo Analysis
In this study, you will perform a statistical analysis of an electronic circuit under variations of

different component parameters. You have to write a MATLAB program to perform all the

analyses.
Procedure
Following the procedure as described in section 5.11 of your text book, design a four-resistor bias

circuit for an npn BJT amplifier to yield a Q-point of ICQ = 75 μA and VCEQ = 5 V. Assume β = 80 for

your npn BJT.

(1) Show your nominal values of all the resistors and the required supply voltage.
(2) Perform a Monte Carlo analysis of your BJT bias circuit considering 10% tolerance of all

the resistors, 5% tolerance of the supply voltage and 50% tolerance of the β value.
(3) Show the histogram plots of ICQ and VCEQ from your Monte Carlo simulation for 50, 100,

200 and 500 iterations. For each case, show the mean and standard deviation of your ICQ
and VCEQ values.
The above analysis is to study the effect of all the variations from your circuit elements.

Sometimes for our design optimization, we focus on the most sensitive element in our circuit,
which is affecting the circuit performance most. The next analysis is to study the effect of

individual element in your amplifier circuit performance. For the previously designed fourresistor bias circuit, consider the following special cases
(a) Case 1: assume only RC and RE have 10% tolerance whereas the rest of the circuit

elements (R1, R2, VCC, β) can maintain their nominal values. Now follow steps (2) and (3)
to study the effects on ICQ and VCEQ.
(b) Case 2: assume only R1 and R2 have 10% tolerance whereas the rest of the circuit

elements (RC, RE, VCC, β) can maintain their nominal values. Now follow steps (2) and (3)
to study the effects on ICQ and VCEQ.
(c) Case 3: assume only β has 50% tolerance whereas the rest of the circuit elements (RC, RE,

R1, R2, VCC) can maintain their nominal values. Now follow steps (2) and (3) to study the

effects on ICQ and VCEQ.
(d) From the above analyses (a, b, c), which one is the most sensitive element for your

amplifier bias circuit and why?
Reference: Microelectronic Circuit Design by Jaeger and Blalock, 5th edition, page number 254.
Report Format:
Cover page, circuit schematic, equations used for calculations, nominal values in tabular forma

assignmentmonte-carlo-s4oap41u.pdf

Answered 1 days AfterNov 04, 2022

Baljit · Accepted Answer

17
MONTE CARLO ANALYSIS OF FOUR RESISTOR  BIAS CIRCUIT FOR NPN BJT AMPLIFIER
Design of 4 Resistor  Bias Circuit
Given data:- Q point of (75uA,5V) i.e ICQ=75uA and VCEQ=5V and  β=80
Assumption:- Supply voltage 15V and VBE=0.7V
Figure 1 Schematic Diagram of 4 resistor Bias Circuit.
Nominal Value Calculations:-
To calculate values for the resistors, we must know the voltage across the emitter and collector resistors and the voltage VB. VCE is designed to be 5 V. One common choice is to divide the remaining power supply voltage (VCC − VCE ) = 10 V equally between RE and RC. Thus, VE = 5 V and VC = 5 + VCE = 10 V. The values of RC and RE are then given by
RC=(VCC-VC)/IC=5/75u=66.66kΩ
                                       RE=VE/IE=5/75.75u=66kΩ               
Now Base Voltage VB=VE+VBE=5+0.7=5.7V.
For Forward Active region IB=IC/β =75/80=0.9375uA
Now Assume I2=10IB  So I1=9IB
So I2=9.375uA and I1=8.4375uA
Now
R1=VB/I1=5.7/8.4375=675.55kΩ
R2=(VCC-VB)/I2=992Kω
Nominal Values
	RC
	66.66kΩ
	RE
	66kΩ
	R1
	675.55kΩ
	R2
	992kΩ
	vcc
	15V
Monte Carlo analysis:-
Matlab Code:-
clc;
clear all;
close all;
n=50; %number of iteration
VBE=0.7; %Base Emitter Voltage
VCC=15*(1+0.1*(rand(n,1)-0.5)); %Supply Voltage
R1=675600*(1+0.2*(rand(n,1)-0.5)); %R1 resistor
R2=992000*(1+0.2*(rand(n,1)-0.5)); %R2 resister
RC=66700*(1+0.2*(rand(n,1)-0.5));  % collector resistor
RE=66000*(1+0.2*(rand(n,1)-0.5));  %Emitter Resistor
b=80*(1+(rand(n,1)-0.5)); % current gain beta
a=b./(b+1);               %alpha gain
VEQ=VCC.*(R1./(R1+R2));    %Emitter Voltage
REQ=(R1.*R2)./(R1+R2);     %Net Resistence
IB=(VEQ-VBE)./(REQ+(b+1).*RE); %Base Current
ICQ=b.*IB;                     %Collector Current
IE=ICQ./a;                      %Emitter Current
VCEQ=VCC-ICQ.*RC-IE.*RE;        %Collector Emitter Voltage
mean(ICQ)                  %mean of Collector Current 
std(ICQ)           %Standrad deviation of Collector Current
mean(VCEQ)         %mean of Collector Emitter Voltage
std(VCEQ)  %Standrad deviation of Collector Emitter voltage
subplot(2,1,1)
hist(ICQ)
xlabel('Iceq')
ylabel('Frequency')
title('Histogram of Ic')
subplot(2,1,

Monte Carlo AnalysisIn this study, you will perform a statistical analysis of an electronic circuit under variations of different component parameters. You have to write a MATLAB program to perform...

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