How Do You Construct Bode Plots for Cascaded CR Networks?

[Dirac8767]

Homework Statement

Question attached

Homework Equations

Frequency response of circuit given in document

The Attempt at a Solution

The question leads me to find the Gain and phase of the gain, pole and zero terms.
The breakpoint frequency and the point where the gain term is 0db.

Gain is 0dB when ω=1rad/s
There is a breakpoint at ω = ω0 rad/s where Gain = -3.01dB

I am having trouble constructing bode plots from this information.

When the system is cascaded with two other models as the question requires

Gain CR = 1×10-6×10×103 = 1×10-2
.
Therefore ω0 = 100rad/s and
Gain dB = -120dB

 

[gneill]

The question seems to be suggesting that you ignore loading effects, which I presume is meant to mean that each LC stage does not impact the operation of the other two. In that case the net transfer function would be the cube of the basic LC transfer function with the given component values.

One way of portraying an approximation for the bode plot of a simple LC filter (i.e. a first order filter) is to sketch a straight-line "schematic" of the actual curve, assuming a 20 db/decade slope beyond the cutoff frequency and a horizontal line at unity gain in the bandpass region.

You could estimate the bode plot of the cascaded units by considering the effect of each stage individually. If the basic LC high pass filter gives an attenuation of 20dB per decade then two will yield 40 db/decade, and three will yield 60 db/decade. A similar argument could be applied to the phase shift vs frequency plot.

Again, this assumes no loading effects between stages. In "real life" the stages will interact and the resulting filter will have a markedly shifted cutoff frequency (3db down frequency) and a much "rounder" shoulder entering the bandpass region.