Chapter 10: Amplifier Frequency Response

Example 10.1, Page Number: 311

In [19]:
import math

A_p=250.0
A_p_dB=10*math.log10(A_p)
print('Power gain(dB) when power gain is 250 = %d'% math.ceil(A_p_dB));
A_p=100.0
A_p_dB=10*math.log10(A_p)
print('Power gain(dB) when power gain is 100 = %d'%A_p_dB)
A_p=10.0
A_p_dB=20*math.log10(A_p)
print('Voltage gain(dB) when Voltage gain is 10 = %d'%A_p_dB)
A_p=0.50
A_p_dB=10*math.log10(A_p)
print('Power gain(dB) when voltage gain is 0.50 = %d'%A_p_dB)
A_p=0.707
A_p_dB=20*math.log10(A_p)
print('Power gain(dB) when power gain is 0.707 = %d'%A_p_dB)

Power gain(dB) when power gain is 250 = 24
Power gain(dB) when power gain is 100 = 20
Voltage gain(dB) when Voltage gain is 10 = 20
Power gain(dB) when voltage gain is 0.50 = -3
Power gain(dB) when power gain is 0.707 = -3

Example 10.2, Page Number: 313

In [20]:
v_out=0.707*10;
print('output voltage in volts at -3dB gain  = %.2f'%v_out)
#at -6dB voltage gain from table is 0.5
v_out=0.5*10;
print('output voltage in volts at -6dB gain = %d'%v_out)
#at -12dB voltage gain from table is 0.25
v_out=0.25*10;
print('output voltage in volts at -12dB gain = %.1f'%v_out)
#at -24dB voltage gain from table is 0.0625
v_out=0.0625*10;
print('output voltage in volts at -24dB gain = %.3f'%v_out)

output voltage in volts at -3dB gain  = 7.07
output voltage in volts at -6dB gain = 5
output voltage in volts at -12dB gain = 2.5
output voltage in volts at -24dB gain = 0.625

Example 10.3, Page Number: 316

In [21]:
import math
R_in=1.0*10**3;
C1=1.0*10**-6;
A_v_mid=100.0;    #mid range voltage gain
f_c=1/(2*math.pi*R_in*C1);
#at f_c, capacitive reactance is equal to resistance(X_C1=R_in)
attenuation=0.707;
#A_v is gain at lower critical frequency
A_v=0.707*A_v_mid;
print('lower critical frequency = %f Hz'%f_c)
print('attenuation at lower critical frequency =%.3f'%attenuation)
print('gain at lower critical frequency = %.1f'%A_v)

lower critical frequency = 159.154943 Hz
attenuation at lower critical frequency =0.707
gain at lower critical frequency = 70.7

Example 10.4, Page Number: 317

In [22]:
A_v_mid=100.0;
#At 1Hz frequency,voltage gain is 3 dB less than at midrange. At -3dB, the voltage is reduced by a factor of 0.707
A_v=0.707*A_v_mid;
print('actual voltage gain at 1Hz frequency = %.1f'%A_v)
#At 100Hz frequency,voltage gain is 20 dB less than at critical frequency (f_c ). At -20dB, the voltage is reduced by a factor of 0.1
A_v=0.1*A_v_mid;
print('actual voltage gain at 100Hz frequency = %d'%A_v)
#At 10Hz frequency,voltage gain is 40 dB less than at critical frequency (f_c). At -40dB, the voltage is reduced by a factor of 0.01
A_v=0.01*A_v_mid;
print('actual voltage gain at 10Hz frequency = %d'%A_v)

actual voltage gain at 1Hz frequency = 70.7
actual voltage gain at 100Hz frequency = 10
actual voltage gain at 10Hz frequency = 1

Example 10.5, Page Number: 319

In [23]:
import math
R_C=10.0*10**3;
C3=0.1*10**-6;
R_L=10*10**3;
A_v_mid=50;
f_c=1/(2*math.pi*(R_L+R_C)*C3);
print('lower critical frequency = %f Hz'%f_c)
#at midrange capacitive reactance is zero
X_C3=0;
attenuation=R_L/(R_L+R_C);    
print('attenuation at midrange frequency = %.1f'%attenuation)
#at critical frequency, capacitive reactance equals total resistance
X_C3=R_L+R_C;
attenuation=R_L/(math.sqrt((R_C+R_L)**2+X_C3**2));
print('attenuation at critical frequency = %f'%attenuation)
A_v=0.707*A_v_mid;
print('gain at critical frequency = %.2f'%A_v)

lower critical frequency = 79.577472 Hz
attenuation at midrange frequency = 0.5
attenuation at critical frequency = 0.353553
gain at critical frequency = 35.35

Example 10.6, Page Number: 321

In [24]:
import math
B_ac=100.0;
r_e=12.0;
R1=62.0*10**3;
R2=22.0*10**3;
R_S=1.0*10**3;
R_E=1.0*10**3;
C2=100.0*10**-6;
#Base circuit impedance= parallel combination of R1, R2, R_S
R_th=(R1*R2*R_S)/(R1*R2+R2*R_S+R_S*R1);
#Resistance looking at emitter
R_in_emitter=r_e+(R_th/B_ac);
#resistance of equivalent bypass RC is parallel combination of R_E,R_in_emitter
R=(R_in_emitter*R_E)/(R_E+R_in_emitter);
f_c=1/(2*math.pi*R*C2);
print('critical frequency of bypass RC circuit = %f Hz'%f_c)

critical frequency of bypass RC circuit = 75.893960 Hz

Example 10.7, Page Number:323

In [25]:
import math
V_GS=-10.0;
I_GSS=25.0*10**-9;
R_G=10.0*10**6;
C1=0.001*10**-6;
R_in_gate=abs((V_GS/I_GSS));
R_in=(R_in_gate*R_G)/(R_G+R_in_gate);
f_c=1/(2*math.pi*R_in*C1);
print('critical frequency = %f Hz'%f_c)

critical frequency = 16.313382 Hz

Example 10.8, Page Number: 324

In [26]:
import math
V_GS=-12.0;
I_GSS=100.0*10**-9;
R_G=10.0*10**6;
R_D=10.0*10**3;
C1=0.001*10**-6;
C2=0.001*10**-6;
R_in_gate=abs((V_GS/I_GSS));
R_in=(R_in_gate*R_G)/(R_G+R_in_gate);
R_L=R_in;    #according to question
f_c_input=1/(2*math.pi*R_in*C1);
print('critical frequency of input RC circuit = %f Hz'%f_c_input)
f_c_output=1/(2*math.pi*(R_D+R_L)*C2)
print('critical frequency of output RC circuit = %f Hz'%f_c_output)

critical frequency of input RC circuit = 17.241786 Hz
critical frequency of output RC circuit = 17.223127 Hz

Example 10.9, Page Number: 327

In [27]:
import math
B_ac=100.0;
r_e=16.0;
R1=62.0*10**3;
R2=22.0*10**3;
R_S=600.0;
R_E=1.0*10**3;
R_C=2.2*10**3;
R_L=10.0*10**3;
C1=0.1*10**-6;
C2=10.0*10**-6;
C3=0.1*10**-6;
#input RC circuit
R_in=(B_ac*r_e*R1*R2)/(B_ac*r_e*R1+B_ac*r_e*R2+R1*R2);
f_c_input=1/(2*math.pi*(R_S+R_in)*C1);
print('input frequency = %f Hz'%f_c_input)
#For bypass circuit; Base circuit impedance= parallel combination of R1, R2, R_S
R_th=(R1*R2*R_S)/(R1*R2+R2*R_S+R_S*R1);
#Resistance looking at emitter
R_in_emitter=r_e+(R_th/B_ac);
#resistance of equivalent bypass RC is parallel combination of R_E,R_in_emitter
R=(R_in_emitter*R_E)/(R_E+R_in_emitter);
f_c_bypass=1/(2*math.pi*R*C2);
print('critical frequency of bypass RC circuit = %f Hz'%f_c_bypass)
f_c_output=1/(2*math.pi*(R_C+R_L)*C3)
print('output frequency circuit = %f Hz'%f_c_output)
R_c=R_C*R_L/(R_C+R_L);
A_v_mid=R_c/r_e;
attenuation=R_in/(R_in+R_S);
A_v=attenuation*A_v_mid;    #overall voltage gain
A_v_mid_dB=20*math.log10(A_v);    
print('overall voltage gain in dB = %f'%A_v_mid_dB)

input frequency = 773.916632 Hz
critical frequency of bypass RC circuit = 746.446517 Hz
output frequency circuit = 130.454871 Hz
overall voltage gain in dB = 38.042470

Example 10.10, Page Number: 330

In [28]:
import math
B_ac=125.0;
C_be=20.0*10**-12;
C_bc=2.4*10**-12;
R1=22.0*10**3;
R2=4.7*10**3;
R_E=470.0;
R_S=600.0;
R_L=2.2*10**3;
V_CC=10.0;
V_B=(R2/(R1+R2))*V_CC;
V_E=V_B-0.7;
I_E=V_E/R_E;
r_e=25.0*10**-3/I_E;
#total resistance of input circuit is parallel combination of R1,R2,R_s,B_ac*r_e
R_in_tot=B_ac*r_e*R1*R2*R_S/(B_ac*r_e*R1*R2+B_ac*r_e*R1*R_S+B_ac*r_e*R2*R_S+R1*R2*R_S);
R_c= 1100.0#R_C*R_L/(R_C+R_L)
A_v_mid=R_c/r_e;
C_in_Miller=C_bc*(A_v_mid+1)
C_in_tot=C_in_Miller+C_be;
C_in_tot=C_in_tot*10**10
f_c=1/(2*math.pi*R_in_tot*C_in_tot);
print('total resistance of circuit = %f Ohm'%R_in_tot)
print('total capacitance = %f * 10^-10 F'%C_in_tot)
print('critical frequency = %f Hz'%f_c)

total resistance of circuit = 377.815676 Ohm
total capacitance = 2.606290 * 10^-10 F
critical frequency = 0.000162 Hz

Example 10.11, Page Number: 333

In [29]:
import math
C_bc=2.4*10**-12;    #from previous question
A_v=99.0;    #from previous question
R_C=2.2*10**3;
R_L=2.2*10**3;
R_c=R_C*R_L/(R_C+R_L);
C_out_Miller=C_bc*(A_v+1)/A_v;
f_c=1/(2*math.pi*R_c*C_bc);    #C_bc is almost equal to C_in_Miller
C_out_Miller=C_out_Miller*10**12
print('equivalent resistance = %d Ohm'%R_c)
print('equivalent capacitance =%f *10^-12 F'%C_out_Miller)
print('critical frequency =%f Hz'%f_c)

equivalent resistance = 1100 Ohm
equivalent capacitance =2.424242 *10^-12 F
critical frequency =60285963.292385 Hz

Example 10.12, Page Number: 334

In [30]:
C_iss=6.0*10**-12;
C_rss=2.0*10**-12;
C_gd=C_rss;
C_gs=C_iss-C_rss;
C_gd=C_gd*10**12
C_gs=C_gs*10**12
print('gate to drain capacitance = %.1f * 10^-12 F'%C_gd)
print('gate to source capacitance = %.1f * 10^-12 F'%C_gs)

gate to drain capacitance = 2.0 * 10^-12 F
gate to source capacitance = 4.0 * 10^-12 F

Example 10.13, Page Number:335

In [31]:
import math
C_iss=8.0*10**-12;
C_rss=3.0*10**-12;
g_m=6500.0*10**-6;    #in Siemens
R_D=1.0*10**3;
R_L=10.0*10**6;
R_s=50.0;
C_gd=C_rss;
C_gs=C_iss-C_rss;
R_d=R_D*R_L/(R_D+R_L);
A_v=g_m*R_d;
C_in_Miller=C_gd*(A_v+1);
C_in_tot=C_in_Miller+C_gs;
f_c=1/(2*math.pi*C_in_tot*R_s);
print('critical frequency of input RC circuit =%.3f *10^8 Hz'%(f_c*10**-8))

critical frequency of input RC circuit =1.158 *10^8 Hz

Example 10.14, Page Number: 336

In [32]:
import math
C_gd=3.0*10**-12;    #from previous question
A_v=6.5;             #from previous question
R_d=1.0*10**3;       #from previous question
C_out_Miller=C_gd*(A_v+1)/A_v;
f_c=1/(2*math.pi*R_d*C_out_Miller);
print('critical frequency of the output circuit = %d Hz'%f_c)

critical frequency of the output circuit = 45978094 Hz

Example 10.15, Page Number: 339

In [33]:
f_cu=2000.0;
f_cl=200.0;
BW=f_cu-f_cl;
print('bandwidth = %d Hz'%BW)

bandwidth = 1800 Hz

Example 10.16, Page Number: 340

In [34]:
f_T=175.0*10**6;    #in hertz
A_v_mid=50.0;
BW=f_T/A_v_mid;
print('bandwidth = %d Hz'%BW)

bandwidth = 3500000 Hz

Example 10.17, Page Number: 341

In [35]:
f_cl=1.0*10**3;    #lower critical frequency of 2nd stage in hertz
f_cu=100.0*10**3;  #upper critical frequency of 1st stage in hertz
BW=f_cu-f_cl;
print('bandwidth = %d Hz'%BW)

bandwidth = 99000 Hz

Example 10.18, Page Number: 341

In [36]:
import math
n=2.0;    #n is the number of stages of amplifier
f_cl=500.0;
f_cu=80.0*10**3;
f_cl_new=f_cl/(math.sqrt(2**(1/n)-1));
f_cu_new=f_cu*(math.sqrt(2**(1/n)-1));
BW=f_cu_new-f_cl_new;
print('bandwidth = %f Hz'%BW)

bandwidth = 50710.653245 Hz