1a) Can you realize different all-pole (*) prototype functions by using the same circuit structures? [max. 0.5p]1b) Suppose your friend says he is designing an analog filter that realizes a fifth-order bandpass transfer function based on Chebychev prototype. What would be your brief and friendly advice? [max. 0.5p]1c) The circuit in Fig. 1b: How would you attenuate the passband gain by 6 decibels without adding another RC op-amp stage? [max.2p](*) All-pole means no zeros in the transfer function.
Question
1a) Can you realize different all-pole (*) prototype functions by using the same circuit structures? [max. 0.5p]1b) Suppose your friend says he is designing an analog filter that realizes a fifth-order bandpass transfer function based on Chebychev prototype. What would be your brief and friendly advice? [max. 0.5p]1c) The circuit in Fig. 1b: How would you attenuate the passband gain by 6 decibels without adding another RC op-amp stage? max.2p All-pole means no zeros in the transfer function.
Solution
1a) Yes, you can realize different all-pole prototype functions using the same circuit structures. The key is to adjust the values of the components (like resistors, capacitors, inductors) in the circuit. By doing so, you can change the poles of the transfer function and hence realize different all-pole prototype functions.
1b) When designing an analog filter with a fifth-order bandpass transfer function based on a Chebychev prototype, it's important to remember that the Chebychev filter has a ripple in the passband. If your application can tolerate this ripple, then go ahead. If not, you might want to consider using a Butterworth filter, which has a maximally flat frequency response in the passband.
1c) To attenuate the passband gain by 6 decibels without adding another RC op-amp stage, you can adjust the feedback resistor in the op-amp circuit. A gain of -6 dB corresponds to a voltage gain of about 0.5. So, you would need to adjust the ratio of the feedback resistor to the input resistor to achieve this new gain.
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Synthesize a lowpass Chebychev filter using the following design steps. step 1) Find a normalized Chebychev function H(s) which has 3 dB passband ripple and at least 55 dB attenuation at normalized frequency Ωs =10. step 2) Denormalize H(s) to ωp = 1 krad/s. step 3) Synthesize the transfer function using one or more active filter stages shown in Figure 1. step 4) Do impedance scaling: Scale the circuit elements so that the capacitances are 100 nF or smaller.
Synthesize a lowpass Chebychev filter using the following design steps.step 1) Find a normalized Chebychev function H(s) which has 3 dB passband ripple and at least 55 dB attenuation at normalized frequency ΩsΩ𝑠=10.step 2) Denormalize H(s) to ωp𝜔𝑝 = 1 krad/s.step 3) Synthesize the transfer function using one or more active filter stages shown in Figure 1.step 4) Do impedance scaling: Scale the circuit elements so that the capacitances are 100 nF or smaller.
A band-pass filter response has
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