The ESR is critical to ripple.
Like all these things, the devil is in the detail. Lets assume that we are
talking about a smoothing capacitor conventional 50/60Hz system, and not a
switcher.
Provided the ESR is significantly less than the total driving impedance (Tx
secondary, reflected primary, diode R etc) there is no significant effect.
Here are some numbers for a supply with a 220uF capacitor fed by 1N4007
diodes from a 333V secondary with a total series resistance of 31 ohms
(typical for valved/tubed applications in classic Tek gear). The current
draw is 100mA.
ESR ripple p-p
0.1 3.7V
1 3.9V
3 4.8V
10 8.9V
So in order to double the p-p ripple you need to have an ESR that is about
30% of the total series resistance feeding it. *For this particular
example*. Note that the waveform becomes much more "spikey" at higher ESR,
and hence the RMS value is much less effected.
Craig
