Thank you for your reply, Jim.
The fact is that there is no peak in the frequency domain (gain curve) until the damping factor
is reduced below 0.707 (= 1/sqrt(2)). But, by definition, the system is then already under-
damped with tendency to ringing. The frequency of this ringing is given by formula:
f = f0sqrt(1 - z2); z = damping factor, f0 = nominal corner frequency of the system.
(f0 = sqrt((1 + RC/RL)/(LC))/(2π) = 1/sqrt(LC)/(2π) in practice.)
Here's some data showing what happens when damping factor is reduced below 1.0 by increasing RL:
damping factor (z) gain at f0 ringing frequency peaking frequency (= f0sqrt(1 - 2z2))
1.0 -6dB no ringing no peaking ; RL = L/(2sqrt(LC) + RCC)
0.707 -3dB 0.707f0 no peaking
0.5 0dB 0.866f0 0.707f0
0.25 +6dB 0.968f0 0.935f0
Peaking frequency is always less than f0. So f0 can be regarded as upper frequency limit in all
cases with z ≤ 1. It depends on RL, but only slightly, and in fact increasing RL makes it smaller.
So, here's the lesson to be learned: increasing RL in order to decrease damping factor below
1.0 will not extend the gain curve, it only puts emphasis on the high frequencies...and causes
high frequency ringing in the time domain!
Now, in the light of all this, what would be the optimal choice for damping factor?
I would opt for z = 1.0, and I think, so would our ears too...
P.S. Optimal RL for my Pickering cartridge is calculated below...for 3 values of C.
L = 930mH, RC = 1.3kΩ
C/pF RL/kΩ f0/kHz
200 33.8 12.1
150 39.0 13.9
100 47.9 17.0