u only need to do what it says The circuit of Figure 1 is an inverting low pass

Question

u only need to do what it says

The circuit of Figure 1 is an inverting low pass filter. The magnitude response of the circuit is |V_ OUT/V_ IN|= R2/R1/ Square root 1+(Omega R2C)^2 In this assignment, we will choose values of R1, R2, and C in the circuit of Figure 1 to meet design requirements set on: Input resistance: the input resistance is the ratio of input voltage to input current for a circuit. In the circuit of Figure 1, the input resistance essentially specifies the resistance R1. DC Rain: the DC gain is, from equation (1). the ratio of R2 to R1. Once R1 is determined from the input impedance requirement, the DC gain specifies the required value for R2. Cutoff frequency: once R2 is known, the cutoff frequency requirement specifies the value of the capacitor Design the circuit of Figure I (e.g. choose values for R1, R2. and C) to meet the following design requirements: Input impedance geq 10k Omega DC gain = 2 Cutoff frequency = 10kHz

Explanation / Answer

ok so

R1 > or equal 10K

and DC gain = R2 / R1 = 2

hence R2 = 2R1

if you choose R1 = 10K then R2 = 20K

given fc = 10KHz so :

1 / sqrt(2) = 1 / sqrt(1 + (2pi fc R2C)2 )

hence ,

2pi fc R2C = 1

so C = 1 / (2pi fc R2)

thus for R2 = 20K and fc = 10KHz you will get :

C = 7.96 x 10^-10 F

=> C = 796 pF

approximately C = 800 pF

so the values are :

R1 = 10K

R2 = 20K

C = 800 pF

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