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In the following circuit, the input signal is , and the components have been chosen such that and
.
The output is at the terminals AB.
 What is the transfer function H( )?
 Find the current in the circuit.
 What is the voltage drop across each element of the circuit?
 Show algebraically that at any instant the potential
difference around the circuit is zero.
 At time , where N=0,2,4,... make a sketch
showing the voltage across each element in the complex plane
and show that the vector sum of the voltage drops is equal to
the voltage supplied.
 Write an expression for .
 What is the limit of as goes to
zero?
 What is the limit of as goes to
infinity?
 What is the corner frequency?
 What is at the corner frequency?
 Make a sketch showing the characteristics of on a loglog plot. Label the slope of the curve
where possible, the corner frequency, and the value of at the corner frequency.
 Describe the high and low frequency behavior in dB/octave.

 Draw a passive LCR lowpass filter and write down the transfer
function of your fourterminal network.
 Determine approximations to the transfer function and filter
corner frequency(s).
 Write the resonance frequency, , in terms
of the corner frequency(s).

Write down the transfer function, , for the network
shown below, and from it find:
 the corner frequency(s) and
 the value(s) of at the corner frequency(s).
 Sketch and the voltage phaseshift as a
function of .
 What type of filter is this?

 What is the transfer function for the following circuit?
 Describe the frequency response at low and high frequencies?
 Sketch the magnitude on a loglog plot.
(label slopes, the corner frequency(s), and )
 What is the signal attenuation for .

 Show that the transfer function of a singlepole RC filter drops
by 3 db at the corner frequency. This is often refereed to as
the 3 db downpoint.
 Design a bandpass RC filter with the transfer function shown
below. rad/s and rad/s are the
3 db downpoints of the RC filter sections. Choose impedances
so that the first section is not much affected by the loading of
the second section.
 Are and the 3 db downpoints of a bandpass
filter?
Next: Diode Circuits
Up: Filter Circuits
Previous: Amplifier with Negative Feedback
Doug Gingrich
Tue Jul 13 16:55:15 EDT 1999