Band Pass Filter Equivalent Components

Question

I am designing a very simple first-order RC band pass filter with cutoff frequencies \$f_l = 0.5 MHz\$ and \$f_h = 4.5MHz\$. I have it pictured below (I'm using 5Spice):

This filter acts the way I want it to. The half power points are around the appropriate cutoff frequencies. For the HPF side of the filter, \$f_h = 1/(2*\pi*100nF*3\Omega)= 0.53MHz\$ and on the LPF side, \$f_l = 1/(2*\pi*1nF*35\Omega)= 4.55MHz \$. Below is the frequency domain plot:

Now, when I change the capacitor and resistance values to something that should yield the same cutoff frequencies, the frequency domain plot looks very different. Here's the modified circuit: And the cutoff frequencies should be \$f_h = 1/(2*\pi*31.8pF*10K\Omega)= 0.50MHz\$ and on the LPF side, \$f_l = 1/(2*\pi*3.54pF*10K\Omega)= 4.50MHz \$. However, not only does the peak of the signal exist at less than -20 dB: -3dB from that peak is not at the correct cutoff frequency:

How can these two configurations yield such different results? They both calculate the correct cutoff values, so why are they different in simulation?

Also, in researching this subject I realize that this is a very poor filter and that I should be using a passive RLC band-pass filter or an active one. I'm new to 5Spice, so please suggest any edits to these pictures and I will make them to make this question more readable.

Answer 1

In your first circuit, the high-pass filter (analysed on its own) has an output impedance not greater than 3 ohm (R1 dictates this). Your low-pass stage has an input impedance not less than 35 ohm (R2 dictates this) and, when looked-at together you can see that the low-pass filter stage is applying very little loading to the high-pass stage and you roughly get what you expected.

In your 2nd circuit with R1 = R2 = 10 kohm the 2nd stage is much more heavily loading the first stage and this screws up the nice response as seen in the first circuit.

If you want to use a simple RLC pass band filter you need to describe what bandwidth you need - it might be that what you want in terms of bandwidth might not be realizable from a simple RLC circuit and you may need to cascade two - then you are back to loading problems.

The best choice is made when you decide what you want in terms of bandwidth and out-of-band rejection characteristics.