ECE 110, Spring 2025, Homework #4, Due May 15, 2025
Problem 1 (15 pts): Draw the magnitude and phase responses ofthe following H(s) using Bode plots.
Problem 2 (0 pts): Refer to circuit in Figure 1. This is a simplified model of a variant of the so-called Common-Emitter Amplifier; the shaded box represents a 3-terminal device called a Bipolar Junc-tion Transistor (BJT) that is a crucial component of the modern electronic world. You will en-counter several such circuits in EE 115A and other advanced circuit classes.
(a) Compute the transfer function, H(s), from the voltage input, iin(t) to the voltage output, vL(t). Do NOT plug in the component values.
For the remaining parts, use the component values provided.
(b) Draw Bode plots ofthe magnitude and phase responses of H(s). (correction needed)
(c) What kind of filtering does H(s) offer?
(c) Suppose iin(t) = 0.02sin(400x106t + π/3) Amperes. What is the steady state output voltage?
(d) Suppose iin(t) = 0.02sin(400x106t + π/3) + 0.4cos(5x109t) Amperes. What is the steady state output voltage?
(e) Suppose iin(t) = 0.3cos(120x109t - π/4) Amperes. What is the steady state output voltage?
Figure 1
Problem 3 (15 pts): Design a first order high pass filter with a cut-off frequency of 10 MHz. The input and output should be voltage signals. Draw Bode plots to show the magnitude and phase re-sponses ofthe filter you have designed. (correction needed)
Problem 4 (15 pts): Design a band pass filter with a center frequency of 100 MHz and a bandwidth of 10 MHz. The input and output should be voltage signals. Draw Bode plots to show the magnitude and phase responses ofthe filter you have designed. (correction needed)
Problem 5: Consider the circuit in Figure 2. We will study the effect of source and load impedances on a de-signed filter. A first order LPF is driven by a source with a non-zero source resistance, RS, and is presented a capacitive load, CL.
Figure 2
(a) (5 pts) What is the transfer function from vin(t) to vo(t)?
Effect of source resistance (set CL=0):
(b) (10 pts) Compare with the ideal 1st order LPF response (RS = 0 and CL = 0). With a non-zero source resistance, is it still a low pass filter? How has the cut-of ffrequency changed compared to the ideal 1st order LPF? How has the filter stop-band attenuation changed? How has the pass-band gain changed?
(c) (0 pts) Design the 1st order RL LPF (i.e. choose R and L) such that the -3dB cut-off frequency of the filter in Figure 2 doesn’t deviate from 10 MHz by more than 10% for any source resistance up to RS = 50Ω .
Effect of load (set RS=0):
(d) (10 pts) Comment on how a non-zero CL effects the filter response i.e. compare with the ideal 1st or-der LPF response (RS = 0 and CL = 0). With a non-zero source resistance, is it still a low pass fil-ter? How has the cut-of ffrequency changed compared to the ideal 1st order LPF? How has the filter stop-band attenuation changed? How has the pass-band gain changed?
(e) (Extra Credt: 10 points) Design the 1st order RL LPF (i.e. choose R and L) such that the -3dB cut-off frequency of the filter in Figure 2 doesn’t deviate from 10 MHz by more than 10% for any load capacitance no larger than CL = 1pF. Hint: The idea is to make the impedance of the parallel combination of R and CL be dominated by R.
Problem 6 (20 pts): Consider the circuit in Figure 3.
(a) (4 pts) Find the transfer function, H(s) = Vo(s)/Iin(s).
(b) (4 pts) Plot magnitude and phase response Bode plots. (correction needed)
(c) (4 pts) Find the maximum gain defined as Hmax = |H(jω)|max.
(d) (4 pts) What kind of a filter is this?
(e) (4 pts) Determine its cut-off frequency (or frequen-cies).
Figure 3
Problem 7: A low pass filter and a high pass filter are connected as shown in Figure 5. The low pass and high pass filters are both simple 1st order RC filters with R = 50 Ohms and cut-off frequencies of 1000 MHz and 100 MHz respectively.
Figure 5
(a) (10 pts) Determine the overall transfer function from vi(t) to vo(t).
(b) (Extra credit 5 pts) What kind of a filter does this represent? Identify cut-off frequencies and/or bandwidth.