Electrical Engineering Asked on October 29, 2021

I am building a low pass filter. This is the equation I’m using to calculate what frequencies I want to pass though, but I have a couple questions on details.

$$

f_c = frac{1}{2pi RC}

$$

What goes into `R`

? Does the resistance of the load (R2) affect R? Say R2 is fixed, are there any rules for selectring R1, like load matching?

^{simulate this circuit – Schematic created using CircuitLab}

This simple circuit can be solved by inspection instantaneously either by using Thévenin as correctly highlighted by Wheatley but also by using the fast analytical circuits techniques or FACTs. Simply consider the circuit for $s=0$ and determine the dc transfer function. Then turn the stimulus off - short the input source - and "look" through the capacitor terminals to determine the resistance $R$ you see in this mode. Multiply the result by the capacitor to get the time constant. For a 1st-order circuit, the inverse of the time constant is the pole $omega_p$ you want. The below drawing illustrates the work:

Then assemble the pieces and write the transfer function in a *low-entropy* form as follows:

Answered by Verbal Kint on October 29, 2021

You can use the Thevenin equivalent circuit to see what your capacitor "sees".

Your capacitor will see an input voltage of **Vin*R2/(R1+R2)** in series with a resistor equal to **(R1||R2)**. Hence your load will affect your voltage amplitude and also your cut-off frequency. If it is a problem, you may use an op-amp configured as a voltage follower between the output of your filter and your load.

Answered by Wheatley on October 29, 2021

If you want to check if the equation is applicable (and what is "R" ?), you should use the definition for the cut-off frequency wo. For this purpose you need the transfer function.

It is a first-order lowpass - hence, the general expression applies:

**H(jw)=Ao/(1+jw/wo)**.

Ao: Transfer function for w=0

wo=1/T with T=time constant of the RC product relevant for discharging the capacitor.

Answered by LvW on October 29, 2021

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