Question

a. Determine R for a series RC high-pass filter with a cutoff frequency (fc) of 8 kHz. Use a 100 nF capacitor. b. Draw the schematic (label Vin and Vout). c. Determine the frequency response H(f) in dB at f = 20 kHz given fc = 8 kHz.

Answer 1

a) 199.04 ohms

b) attached in image

c) -0.696dB

Step-by-step explanation:

We are given:

Fc = 8Khz = 8000hz

`C = 100nF = 100*10^-^9F`

a)Using the formula:

`F_c = (1)/(2pie*Rc)`

`8000= (1)/(2*3.14*R*100*10^-^9)`

`R =(1)/(2*3.14*100*10^-^9*8000)`

R = 199.04 ohms

b) diagram is attached

c)
`H(w) = (V_out(w))/(Vin(w)) = (1)/(1-j(wc)/(w))`

`H(F) = (1)/(1-j(fc)/(f))`

At F = 20KHz and Fc= 8KHz we have:

`H(F)= (1)/(1-j(8)/(20)) = (1)/(1-j(0.4))`

`|H(F)|= (1)/(√(1^2+(0.4)^2))`

=0.923

|H(F)| in dB = 20log |H(F)|

=20log0.923

= -0.696dB