high pass filter : cap -> resistor or resistor->cap

[Wounded Paw]

Looking at a certain very old circuit I've seen the input cap in two different configurations

A. input -> 22k resistor -> 10u cap

B. input -> 10u cap -> 22k resistor

I've run both through a spice program and gotten the exact same frequency response.  Is it safe to say that there's absolutely no difference?  The formula for frequency doesn't seem to care which order they're in either.

[John Lyons]

The roll off frequency is the same for both but the placement components is different.
For a low pass you have the resistor in series and the cap to ground, taking the output from the junction of the two.
For a high pass you have the cap in series and the resistor to ground, output taken from the junction of the two.
You can also have a low pass with a resistor between the cap to ground which makes the filter " shelving". Rolling off the high end but only to a point. Making the resistor to ground larger and the cap bigger eats up more high end and into the upper mid range.


John

[Wounded Paw]

hmm,  the circuit I was talking about goes

A. input -> 22k resistor -> 10u cap -> base of NPN transistor and 100k resistor to ground

or

B. input -> 10u cap -> 22k resistor -> base of NPN transistor and 100k resistor to ground


So in case A the cap and 100k resistor are a high pass but so is B if you ignore the 22k resistor.  I'm still not sure of the difference between the two.

[John Lyons]

The cap is a DC blocking cap and the 22K is an impedance setting resistance.
It will cut down on some level as well working as a voltage dividerwith the 100K to ground.
The cap also sets a low pass roll off but it's pretty low at 10uf.

I don't think there is any difference in the different R/C order.

[George Giblet]

> 22k resistor -> 10u cap

Let me get this right.  The 22k and 10uF cap in series right?  First thing in any circuit if you swap the order of series components it has no effect.

Here's some same examples:

http://www.geocities.com/george_giblet/effects/lpfhpf_ckt.png

and the response,

http://www.geocities.com/george_giblet/effects/lpfhpf_resp.png

The first two circuits LPF and HPF are idealized circuits. You can calculate the -3dB frequency from f3 = 1/(2*pi*R*C) = 1/(2*3.1416*50k*10uF) = 0.32Hz, which is what is shown on the frequency response plots.  I've picked a different R here because drawing parallel between the circuits has a fewq quirky details.

In case A and case B the response is the same.  The circuit here is a high-pass filter, however there are two resistors instead of the single resistor in the idealized circuit.   If you compare circuit B against the HPF circuit you can see the capacitor "works against" the series combinations of the 22k and the 100k in series ie. 122k.  If you looked at the point between C3 and R5 it would be a high-pass filter with C=10uF and R=122k ie. f3 = 1/(2*pi*10uF*122k) = 0.13Hz.  The output terminal is that point feed through a divider formed by the 100k resistor and the 22k resistor.  The division ratio is 100k/(22k+100k) = 0.82 or -1.72dB.   So what you have is a high-pass filter and a divider in one.  If you look at the frequency repsonse curve of B (or A) you can see the response flattens out to about -1.7dB.  The -3dB point is -3dB below the -1.7dB line or -4.7dB, from the plot you can see this is about 0.13Hz.

Case C is the LPF connection of the parts in A.    This version is little harder to understand.  At low frequencies the capacitor can be removed and you end-up with a voltage divider formed with the 22k and the 100k which gives you a baseline attenuation of -1.7dB, which is seen at the left of the C frequency response trace.   To understand what R to use you need to understand Thevenin equivalent circuits. This turns out to be the 22k *in parallel* with the 100k ie. 18k.  So if you calculate the -3dB point you get 1/(2*pi*18k*10u) = 0.88Hz.  As with case A/B the -3dB point on the response plot is -3dB below the -1.7dB baseline, which again is -4.7dB.

You should realize that you have to use the correct R's cut-off to calculate the point for the HPF case (0.13Hz), and this is much different to the LPF case (0.88Hz).  With the idealized circuits the cut-off is the same in each case ie. 0.32Hz.   The reason is on the idealized case we are flipping both the R and C but in Case A/B we only move the cap and the resistors stay fixed.   The role of the resistor changes.

Here's a quick way to get the -3dB point:
- In case A/B you approximate the circuit by making it look like the idealized HPF circuit, you do this by removing the 22k.  You argue that the 22k is smaller than the 100k and therefore has little effect.  In this case you get a -3dB frequency of 1/(2*pi*100k*10uF) = 0.16Hz, not bad compared to the exact 0.13Hz.
- In case C you approximate the circuit by making it look like the idealized LPF circuit, you do this by removing the 100k.  You argue that the 100k is larger than the 22k and therefore has little effect.  In this case you get a -3dB frequency of 1/(2*pi*22k*10uF) = 0.72Hz, not bad compared to the exact 0.88Hz.