When feeding an RF signal to a coaxial transmission line, when do you have to take into consideration the capacitance of the cable? I am working with a 36 MHz signal. The total cable length is ~3 ft (RG316 with SMA connectors).
The source and load impedances are not equal. The source impedance is -130\$j \Omega\$ and the load impedance is 1 k\$\Omega\$.
I want to make sure I am calculating the transfer function correctly.
50 ohm air spaced cable has a capacitance of 66.7pF/m, dielectric spaced cables with velocity factors around 0.66 have around 100pF/m. This is a useful number, every time you connect two items together in the lab with a typical 1m coax cable, at low frequencies it is like adding 100pF across the signal. A 2m cable is like 200pF.
\$C=\frac{1}{Z_0 v}\$ where \$v=\frac{c}{\sqrt{\epsilon_r}}\$ is the velocity of propagation
As your 1m cable is around 20% of a wavelength at 36MHz you should really treat it as a transmission line.
Just looking at the capacitance, at low frequencies it looks like about 100pF, which at 36MHz has a reactance of about 44ohms. It is clearly going to influence your circuit where your impedance is around 1k.
Assuming that you are after the simple voltage transfer function from a source with 130k impedance to the 1k load, with no cable you have -42.3dB. Treating the cable as a simple 100pF shunt gives -69.4dB, treating it as a 5ns length of 50 ohm cable gives -67.4dB (from a simple SPICE sim).
Assuming that you are after the simple voltage transfer function from a source with -130j impedance (= 34pF cap at 36MHz) to the 1k load, with no cable you have -0.1dB. Treating the cable as a simple 100pF shunt gives -11.9dB, treating it as a 5ns length of 50 ohm cable gives -8.9dB (from a simple SPICE sim). Note that this can change quite dramatically with the length of the cable, use a 2m cable and you get -2.8dB, increasing your signal by over 6dB.
An RG316 cable has a transmission velocity at 0.69 times the speed of light (ref) which makes the cable length of 3 feet well over 0.1 times the wavelength.
Treating the cable capacitance as a lumped capacitance probably won't be too accurate, and it's better to treat the cable with a more accurate model - distributed inductance and capacitance which make for a transmission line with a particular impedance (probably 50 ohms). This analysis can be done using a smith chart and can be used to yield the impedance that the source sees when looking at the cable and all of its length, plus the load attached at the far end.
Cable capacitance is always present. The following link characterizes the capacitance of RG316 coaxial cable as 32 pF/m. It lists the frequency response as DC to 3 GHz.
https://www.pasternack.com/images/ProductPDF/RG316-DS.pdf
The frequency response of SMA connectors is listed at the following link as 18 GHz.
Operating at 36 MHz is well within the operating ranges of your cabling components.
The source and load impedances (in particular, the mismatch) will limit the frequency response of your system. Your source impedance doesn't appear to be realistic.
If one would see the different behavior for "distributed" or "lumped" (1 section) parameters, here are two pictures for "amplitude" and "phase". Unless "errors" are always possible.
The number of the section is here 1, so the same "behavior" (line or lumped) is not "respected". More sections are thus needed. See results @36MHz.
