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.

Step 1: Find a normalized Chebychev function H(s)

The Chebyshev filter is defined by its passband ripple and stopband frequency. The passband ripple is 3 dB and the stopband frequency is 10 (normalized). The attenuation in the stopband is 55 dB.

To find the order of the filter, we can use the Chebyshev filter formula:

N = acosh[((10^(0.1As) - 1) / (10^(0.1Ap) - 1)]^0.5 / acosh(Ws)

where As is the stopband attenuation (55 dB), Ap is the passband ripple (3 dB), and Ws is the stopband frequency (10).

Solving this equation will give us the order of the filter.

Step 2: Denormalize H(s) to ωp = 1 krad/s

The transfer function H(s) can be denormalized to the desired frequency by replacing s with s/ωp in the transfer function, where ωp is the desired frequency (1 krad/s in this case).

Step 3: Synthesize the transfer function using one or more active filter stages

The transfer function can be synthesized using active filter stages. This involves breaking down the transfer function into second order sections, and implementing each section with an active filter stage.

Step 4: Do impedance scaling

Impedance scaling involves scaling the resistors and capacitors in the circuit so that the capacitances are 100 nF or smaller. This can be done by multiplying all resistors by a scaling factor k, and dividing all capacitors by the same factor. The value of k should be chosen such that the largest capacitor value is 100 nF.

Please note that the actual calculations and circuit design would depend on the specific values obtained in the previous steps.