? Which of the following correctly expresses the magnitude of the transfer function for the series RC low-pass filter? 1/RC √² + 1/RC w²+ RC 1 --)² RC √²+1 = = = 1² RC 1 + RC 1 RC w² + (- RC -)²

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C4 10n U1 R1 R2 Vou 10k 10k V1 C3 10n AC 1 .ac dec 50 10 10k .lib opamp.sub Determine the resonant frequency fo in Hz of the lowpass filter shown above.

1. Draw the complete bode plot of a 1st order active LPF given below. V R = 15K :C=0.02µF R₂ = 27K wwwwww R₁ = 3.3K V₂ Required: Complete bode plot of the filter.

4. Consider the circuit shown on the right. a) Determine the filter type. 22 uF 100 mH b) Calculate Q, B, wc1, wc2, and wo. c) Is this circuit a narrow-band or a wide-band filter? Vi(t) 390 Ω 90 ΚΩ 10 ΚΩ V₂(1)

1. A) B) Write the transfer function for the RC high-pass filter of Figure 2. First write it in terms of jw (or s) and then write it as its magnitude and phase angle. Determine and record below the cutoff frequencies of the circuit. Sketch the straight line approximations of the frequency responses for the RC high-pass filter on Graph Avla 0.1 0 -20 -10 90° 60° 30° 0' -30° -60* -90* e=2 sin (cot) 0 0.2 (a) Voltage gain response 0.5 0.1 0.2 b.² (b) Phase shift response 1 1 R = 75 ohms 2 L=2.4 mH 5 Vout 10 20 10 20 50 50 100 f (kHz) 100 (kHz)

1. Obtain the transfer function. Identify the type of filter the circuit represents and determine the corner frequency. Take R₁ = 100 = R₂, L = 2 mH. R₁ v;(1) R₂ rell L www 1

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Magnitude (dB) Phase (deg) 0 -5 -10 -15 -20 -25 -30 -35 -40 -15 -30 -45 -60 -75 -90 10 Bode Diagram Frequency (Hz) Assume an RC circuit filter has the bode plot shown above. 10* In units of dB, what is the magnitude of the transfer function at f = 900 Hz, |H(f = 900 Hz)|dB? |H(f = 900 Hz)|dB [dB] : _~15 rad B) In units of what is the approximate cut-off frequency, we, for the RC circuit? Do not leave sec' your answer in terms of . rad. We []:

Determine the transfer function that produced the following Bode plot. (Note: the values here were chosen so that this transfer function could be determined exactly): 120 Bode Diagram 100 80 60 40 20 45 -90 -135 -180 100 10 102 10 Frequency (radis) 10 (ge) pronbep (Bop) oe