I studied EE in college back in the '90s, and have a grasp on the general concepts, but am a bit out of touch with details.

I'm trying to size some DC blocking caps and am trying to remember the math behind RC frequency response. I know, in general, the higher the impedance (either by resistance or capacitance), the lower the frequency response. That is, if you're cutting off too much low end, you can either make the cap bigger, or increase the impedance on the load (both of which have side effects, so you have to be careful with which one you choose.)

I went in search of the specific numbers to back this up and found

this article which links to

this page of a ton of math that eventually boils down to:

The cut-off (read: half point) frequency of an RC circuit is: f_c = 1/(2*Pi*R*C)

Which agrees with my general understanding: Increase either the R or the C and the frequency response lowers. So, let's say I was building

a simple tube headphone amp which is

notoriously bright and lacking a bit in low end, and I wanted to calculate what the frequency response of the DC blocking caps on the front and back end were.

The front end is a 2.2uF cap, to a 100kOhm resistor to ground, and the grid of the tube (which has "a very high impedance," probably higher than 100kOhm, so we'll ignore it here.) Our equation above would give us:

f_c = 1/(6.28*0.0000022*100000) = .72Hz

Uhh.. Really? Even if the grid were 10k, the response would still be 7.2Hz. Am I doing my math correctly here? Specifically, that the DC blocking cap is _NOT_ the source of the missing low end?

Similarly, the output drives a 470uF cap to your headphone load (likely lower than the 1k bleed cap, which we'll ignore) which is

50 ohms in my case. This gives us:

f_c = 1/(6.28*0.000470*50) = 6.8Hz

10x the input, but still less than 1/2 the response of the headphones, and 1/3 the response of my ears.

Does anyone see anything wrong with my math here? That .72Hz seems suspect, but the 6.8Hz seems reasonable. Thanks for your help.