# Are these two circuits the same?

Are these rwo circuits the same considering the right hand sides of them where it is parallel for the C&R and C&L(meaning the way i should obtain the frequency response? And for the longer circuit how do i obtain the frequency response and the freqency for MAX amplitude response(im lost with the second one)

• The second one passes DC. The first one does not. Therefore they are not the same. – Transistor Dec 26 '18 at 14:42
• may be similar but never the same, at high f, C1/(C1+C2) dominates – Sunnyskyguy EE75 Dec 26 '18 at 14:42
• @Transistor no. The second one doesn’t pass DC. It short-circuits it to ground. – Edgar Brown Dec 26 '18 at 16:30

These two circuits can provide similar bandpass frequency response.

However, the lower-frequency cutoff must be considerably lower than the high-frequency cutoff. This means that the frequency span of the pass-band must be wide, if these two circuits are to provide similar results. For bandpass response with narrow pass-band, the LC circuit is king. Note that the RC bandpass cannot provide anywhere near as much output power as the LC bandpass - it must see a very high-impedance load.

Here's an example to illustrate similar bandpass response of the two circuits (both these examples deliver no power to a load):

If you know the corner frequency of the low-pass edge, and you know the corner frequency of the high-pass edge, I think the centre frequency of maximum response would be the geometric mean: $$\ \sqrt{f_{lower} f_{upper}} \$$

For the RC circuit, upper corner frequency is near $$\ 1 \over {2 \pi R_1 C_2} \$$ while lower corner frequency is near $$\ 1 \over {2 \pi R_2C_1} \$$

Edit:
To get identical response I've added a loading resistor to the LC version (R5:9.091K), and I've added a different loading resistor to the RC version (R4:200K). The value of R2 was changed from 100k previously to 200k, to preserve the lower corner frequency). Now frequency response is identical:

• You might provide a description of input and output impedances at DC -- where the circuits behave strikingly different. – Scott Seidman Dec 26 '18 at 17:40
• @ScottSeidman Both LC & RC filters have similar response at low frequencies: they both drop at 20 dB/decade (no matter how you load them). Response of both at DC is infinite attenuation. Load resistances tend to affect the corner frequencies & mid-band attenuation. – glen_geek Dec 26 '18 at 18:01
• "The same" is what the OP asked. Circuit one has an (ideal) infinite input impedance at DC, and Circuit 2 has an input impedance of R at DC. If nothing else, this can certainly impact your choice for R. Practically, you'd also want to know how you'll be driving each circuit. Not saying you're wrong, or off, but just giving you the opportunity to highlight the differences. – Scott Seidman Dec 26 '18 at 18:14