Feedback question

[smbrown]

I'm sure the answer is going to be a lot more complex than my simple question, but here goes. Let's say we have a PP UL EL-34 amp using good iron. How does one decide how much feedback (or any) is correct? My experience is that less really is more, but what's the "right" amount? Do we go for a particular damping factor? Bandwidth? etc.. Also, if someone could show me the math, I'd appreciate it. For example, without feedback a 0.5v input = 30w out, but with feedback a 1v input = 30w out... how many db is that?
Thanks!

[TheGimp]

After having read Beam Power Tubes by O.H. Schade, and Morgan Jones Tube Amp Design, I have come to the conclusion that most amps will do best with -6 to -20dB of GNFB.

Beyond 20dB there seems to be a detremental effect on the noise floor of the amp if I remember correctly.

Now if you are talking about local feedback instead of Global NFB, that is a different matter.

A doubling of input voltage for the same output power would take -6dB of GNFB.

As to how to decide damping factor, bandwidth effects etc, from my understanding they are interrelated and one has to make trade-offs.

[Sch3mat1c]

1. Nix the UL -- it simply doesn't work as good. If you want power, go with pentode and gNFB. If you want Tube Sound, go with triode mode and little or no gNFB (this works best if you have very sensitive speakers, as triode mode puts out 2-5 times less power than pentode mode).

2. Typical amount of gNFB is 20dB. Less and distortion is only covered half-assed, so that THD is somewhat lower, but you get a lot of IMD products (i.e., the distortion is being distorted!), which could sound worse. More NFB keeps THD down enough that higher order distortion is inaudible. Use as much as you want, up to the stability margin: too much and you'll get motorboating at LF (due to coupling capacitors, OPT inductance, and power supply filtering) and overshoot or oscillation at HF (due to plate, grid and OPT capacitances). Because of this, the open-loop gain must fall towards the edges of bandwidth (at LF and HF), which means 20dB NFB needs amp gain to fall to about 1 at whatever point phase shift reaches 180 degrees (this can be measured).

Taking typical SWAG values, let's say you have two coupling capacitors at 0.1uF, working into grid leaks of 100kohms, and the OPT is 50H at 5kohms. These RC and R/L time constants happen to be the same (tau = 10ms), so the total phase shift is 60*3 degrees when Xc = sqrt(3)*R or 9.2Hz, at which point the gain will be down by only 8 (1/2 from each). With more than 18dB NFB, this circuit will make an excellent phase shift oscillator at 9.2Hz. With less, it will have an unexpected LF rise, which if you are not specifically looking for it, may go completely undiscovered through ordinary testing, until one day you walk in and find this amplifier doing your speakers doggy-style at 9Hz!

A similar process applies at high frequency. Let's say you have a 12AX7 driving a triode (an unusual choice, which will help to exaggerate my point slightly), so R ~ 40kohms (taking Rp || RL || Rg) and effective C is around 50pF, for a cutoff point around 80kHz. As for the OPT, it can be difficult to treat, but based on a typical model of leakage inductance, parasitic capacitance and load resistance, choosing realistic values, some analysis can still be made. Let's say it has an HF peak at 30kHz, amplitude about twice the midband value (i.e. Q ~= 2), which is going to be maybe 10kHz wide. At 5kohms primary impedance, the leakage inductance and parasitic capacitance will come out to about 18mH and 750pF. Since these poles are at different frequencies, the same kind of simplified phase shift calculation doesn't apply, however you can still guess that the phase shift will become large in the 30-40kHz area, accentuating the OPT's existing HF rise and causing ringing on square edges (or worse, it goes completely unstable, particularly for nasty loads). Adding a zero to the system can improve the system, and this usually consists of an R+C network connected in parallel with the signal somewhere (usually across the output), or an R || C network in the feedback path. These change the frequency response in various ways, which can improve or worsen the closed-loop response.

Tim