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Circuit Diagrams, Pole Frequencies, and Bode Plots

Not exactly sure how to go about solving the attached problem - concepts include circuit diagrams, pole frequencies, and bode plots.

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Please see the 2 attachments.

1. The first order high pass filter is shown below

Note that I have drawn this as 2 general impedances and as shown.

In this particular case since is a pure resistance we can say its impedance is simply

Similarly the impedance being a pure capacitance has an impedance given by where is the angular frequency of operation of the driving source and is the complex operator telling us that current and voltage are not in phase through such an impedance.

Moreover and to simplify the analysis we can substitute the parameter to obtain the impedance if we wanted to.

GENERAL TRANSFER FUNCTION EXPRESSION:

The output voltage is just given by the voltage divider rule for 2 impedances (in this case and in series) and taking the output voltage as over the impedance .We can therefore write the output voltage as measured across impedance using the voltage divider rule, thus

And as a result we can then write the transfer function as the ratio of to by re-arrangement of the above equation to get

Substituting in our impedance values derived earlier and we obtain

Multiplying top and bottom by (which doesn't change the value of the above as this is equivalent to multiplying by 1) we can write

Which when ...

Solution Summary

The circuit diagrams, pole frequencies and bode plots are examined in the solution.

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