Answer Happy

EXERCISE : (Frequency Response) The circuit’s input represents
the power supply voltage 𝑉𝑠 (𝑡). The circuit’s output is
the resistor’s voltage Vo(t), and it’s transfer function is the
following:
𝐻(𝜔) = Vo(𝜔)/(Vs(𝜔))
The parameters are unknown, so their values need to be
determined. That way the circuit will act as a pass-band filter.
It’s known that the transfer function should have a maximum value
in between 10 and 40 [dB], and that there are factory capacitors
with the following electric capacitance; 𝐶 =
10[𝜇𝐹], 𝐶 = 20[𝜇𝐹], 𝐶 = 30[𝜇𝐹] y 𝐶 =
50[𝜇𝐹].
You must pick one of these specifications.
Pass-band filter. The requirements for the pass-band filter are:
Cutoff Frequencies:
𝜔c2=102[𝑟𝑎𝑑/𝑠 ] 𝑦 𝜔c1= 98
[ 𝑟𝑎𝑑/𝑠 ]
Q Factor between 10 < 𝑄 < 50.
1) is needed. Find the circuit parameters that meet the
required specifications. Graph it’s ideal bode plot and compare it
with the simulated plot.
2. 𝐻(𝜔)’s value for a 10%, 50% 75%, 100%, 125% 150%
frequency, and 200% from the resonance frequency. Tabulate and
compare with the simulated values and explain their
decrease.
3. If the maximum input has a value of 𝑉𝑚á𝑥 =
120[𝑉] at the resonance frequency, what will be resistor R2’s
maximum voltage value? Calculate the magnitude and obtain its phase
relationship. Compare it with the simulated value.
4. If now, the input has the same voltage level, but with a
frequency which is the 10% of the resonance, how much will the
output decrease, in respect to the previous subsection? Comment
about it.
5. How will the Q factor affect the filter? Which is more
convenient, a higher Q factor or a lower Q factor? Which parameters
should be modified in order to increase or decrease the Q
factor?
R L + I Vs(t) • Rr. Ia R2 V.(t)