2. Determine the overall voltage gain (in dB) of the 4th order Band pass filter. Given R7 = 8.9kΩ and R3 = 5.6KΩ.
C1 = 68nF
C2 = 68nF
C5 = 150nF
C6= 150nF
R1 = 10KΩ
R2 = 10KΩ
R4 = 10KΩ
R5 = 47KΩ
R6 = 47KΩ
R8 = 10KΩ
The options are:
a) 10.8 dB
b) 3.2 dB
c) 9.4 dB
d) 6 dB
The formula for voltage gain of a Band pass filter is:
A = (R5/R1) * (1/(R2*C1*C2*R3 + R2*C1*R5 + R3*C2*R6 + 1))
Plugging in the given values,
A = (47KΩ/10KΩ) * (1/((10KΩ*68nF*68nF*5.6KΩ) + (10KΩ*68nF*47KΩ) + (5.6KΩ*68nF*47KΩ) + 1))
A = 0.4019 or 20log(0.4019) = -9.42 dB
The overall voltage gain of the 4th order Band pass filter is -9.42 dB, which is approximately 9.4 dB (option c).
To determine the overall voltage gain of the 4th order Band pass filter, we need to calculate the individual voltage gains of each stage and then multiply them together.
Step 1: Calculate the voltage gain of the first stage (R1 and R2) using the formula Av1 = -R2 / R1.
Given R1 = 10KΩ and R2 = 10KΩ.
Av1 = -R2 / R1 = -10KΩ / 10KΩ = -1.
Step 2: Calculate the voltage gain of the second stage (R3 and R4) using the formula Av2 = -R4 / R3.
Given R3 = 5.6KΩ and R4 = 10KΩ.
Av2 = -R4 / R3 = -10KΩ / 5.6KΩ ≈ -1.79.
Step 3: Calculate the voltage gain of the third stage (R5 and R6) using the formula Av3 = -R6 / R5.
Given R5 = 47KΩ and R6 = 47KΩ.
Av3 = -R6 / R5 = -47KΩ / 47KΩ = -1.
Step 4: Calculate the voltage gain of the fourth stage (R7 and R8) using the formula Av4 = -R8 / R7.
Given R7 = 8.9KΩ and R8 = 10KΩ.
Av4 = -R8 / R7 = -10KΩ / 8.9KΩ ≈ -1.12.
Step 5: Calculate the overall voltage gain by multiplying the voltage gains of each stage, Av = Av1 × Av2 × Av3 × Av4.
Av = -1 × -1.79 × -1 × -1.12 = 3.20
Step 6: Convert the voltage gain to dB using the formula Av(dB) = 20log(Av).
Av(dB) = 20log(3.20) ≈ 9.43 ≈ 9.4 dB.
Therefore, the overall voltage gain of the 4th order Band pass filter is approximately 9.4 dB. Hence, the correct option is c) 9.4 dB.