Q1. Determine the transfer function of the filter 

For the circuit below, determine the transfer function v_{out}(s)/v_{in}(s) where s is the Laplace variable. 

Q9. Find the gain

A second-order low-pass filter has poles in the Laplace variable s  at -0.25\pm j and a transmission zero at \omega= 2.5 \text{rad}/\text{s}, where \omega is the Fourier variable. If the DC gain is unity, find the transfer function T(s). What is the gain of the filter when \omega approaching infinity.

Q8. Find the filter type and transfer function

A filter has transmission zeros at \omega = 2\text{rad}/\text{s} and \omega = \infty, where \omega is the Fourier variable. Its poles are at s = -1 and s = -0.5 \pm j1.0, where s is the Laplace variable. The dc gain is unity. Find the type and transfer function T(s). 

Q7. Find frequency that gives maximum gain

The bandpass filter given below has the transfer function  T(s) = v_{out}(s)/v_{in}(s) where s is the Laplace variable. At what frequency \omega~\text{rad}/\text{s} (where \omega is the Fourier variable), the gain of the filter is maximum?

Q6. Find the resistance

The filter given below is known as an all pass filter. If T(s) is the transfer function v_{out}(s)/v_{in}(s) of the filter where s is the Laplace variable, first find |T(\omega)| and angle T(\omega), where \omega is the Fourier variable. If the desired phase shift is -30^o (-30 degrees) at operating frequency of 5\times10^3\text{rad}/\text{s}, what is the value of R if C=10\text{nF}?

Q5. Find the filter magnitude response

A filter has a transfer function T(s) = \frac{1}{(s+1)(s^2 + s+1)} , where s is the Laplace variable. What is the filter magnitude |T(\omega)| where \omega is the Fourier angular frequency . 

Q4. Find the amplitude and phase of the signal through the filter

A sinusoid with 1\text{V} peak amplitude is applied at the input of a filter having the transfer function \frac{2\pi\times 10^4}{s+ 2\pi\times 10^4} , where s is the Laplace variable. Fine the peak amplitude and the phase (relative to that of the input sinusoid) of the output sinusoid if the frequency of the input sinusoid is 10\text{kHz}.

For the filter below, determine the condition which gives real poles to the transfer function v_{out}(s)/v_{in}(s) where s is the Laplace variable. 

Q2. Determine the type and poles and zeros of the filter

For the circuit below, determine poles and zeros of the transfer function v_{out}(s)/v_{in}(s) where s is the Laplace variable. What type of filter is this?

Q1. Determine the transfer function of the filter 

For the circuit below, determine the transfer function v_{out}(s)/v_{in}(s) where s is the Laplace variable.