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## Homework Statement

Design a filter that will pass frequencies greater than 20 Hz and set the -3dB point at 10 Hz. Assume zero source impedance and 10k load impedance.

## Homework Equations

##f=\frac{1}{2\pi RC}## which is the equation used to determine the 3 dB frequency of an RC filter.

## The Attempt at a Solution

Select a high-pass RC filter. Active filters have no been presented yet in the text, so I am using passive components.

As the input impedence of the load is assumed to be 10k, then I would like the output impedence of my filter to be about 1k: a tenth of the load.

Deriving the output impedence of the high-pass filter:

[itex]

Z_{input}=\frac{Z_{C} R}{R+Z_{C}}=\frac{\frac{R}{j\omega C}}{R+\frac{1}{j\omega C}}=\frac{R}{j\omega R C +1}

[/itex]

The next step is where my thinking is unclear. While I know that I want this output impedence to be about 1k, what kind of value should I select R to be and why? Does the 3 dB frequency I am designing for affect this in any way or is it independent?

Arbitrarily assuming an R value of 1k to match the impedence I want yields the following:

## \frac{1}{C}=2\pi fR## so ##C=\frac{1}{20\pi R}=16 pF##

The design is complete.

The information I am looking for is how to select an R value and why.

Thank you in advance.