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 = f_{0}sqrt(1 - z^{2}); z = damping factor, f_{0} = nominal corner frequency of the system.

(f_{0} = sqrt((1 + R_{C}/R_{L})/(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 R_{L}:

damping factor (z) gain at f_{0} ringing frequency peaking frequency (= f_{0}sqrt(1 - 2z^{2}))

1.0 -6dB no ringing no peaking ; R_{L} = L/(2sqrt(LC) + R_{C}C)

0.707 -3dB 0.707f_{0} no peaking

0.5 0dB 0.866f_{0} 0.707f_{0}

0.25 +6dB 0.968f_{0} 0.935f_{0}

Peaking frequency is always less than f_{0}. So f_{0} can be regarded as upper frequency limit in all

cases with z ≤ 1. It depends on R_{L}, but only slightly, and in fact increasing R_{L} makes it smaller.

So, here's the lesson to be learned: increasing R_{L} 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 R_{L} for my Pickering cartridge is calculated below...for 3 values of C.

L = 930mH, R_{C }= 1.3kΩ

C/pF R_{L}/kΩ f_{0}/kHz

200 **33.8** 12.1

150 **39.0** 13.9

100 **47.9** 17.0