SPICE Analysis of Randall 2 DRD Amplifier

Author: Dmitry Nizhegorodov (dmitrynizh@hotmail.com). My other projects and articles

1.   Introduction

In this article we use PSPICE to explore some of the properties of Randall-2 amplifier, which is a design based on Jack Elliano Direct Reactance Drive (a.k.a. DRD) and Ultrapath ideas. 40+ of these amplifiers were built with a success by Bay Area tube enthusiasts at a class at the SF Randall Museum.

2.   Schematic and parts

Randall-2 is a DRD Ultrapath topology that uses 6an4 for the driver stage and 300B as the power tube. Here is Randall-2 schematic with PSPICE-computed static voltages and currents:

The transformer is 3K:8. Note that we run simulation with a single 6an4 whereas Randall-2 employs 2 triodes connected in parallel, and for that reason the biasing resistor is lower. We also do not show the grid stopper resistors.

3.   Distortion analysis

Using our distortion plotting techniques [1] we obtained the following data:

Clipping starts above 12 WRMS, which is an excellent result for a 300b SET amp. Before 10W, THD is close to 1%. Seems too good to be true, but there is an explanation for it. Note that the levels of the second and the third harmonics are comparable. I will not reveal a big secret if I tell that Randall2 as well as the original DRD by Jack Elliano employ a THD cancellation technique (THDC), and the choice of 6an4 - an unlinear device - as the driver tube was to injects "just enough" harmonics complementary to harmonics of 300b. THDC is never perfect, though. It greatly reduces 2nd harmonic but the price to pay for that is higher products, hence THDC should be used with caution. THDC changes sonic signature of SET amplifiers making them sound half way between SET and PP. Whether it is great or not so great depends on personal listening preferences. With more linear driver tube such as 6sn7 the DRD circuit would produce higher THD but the spectrum would be more "conventional" for SET amps, with 3rd that is 10..15 dB under the 2nd. Low 2nd and fairly high 3rd give DRD its characteristic sound - assertive, refined, definitely not "tubey".

4.   Parametric analysis

In this section we study how small changes to biasing, load, etc. affect the amplifier's distortion spectrum.

4.1   300B bias tap sweep

The tap in the bias of 300B tube that provides B+ to the driver tube is one of the main adjustment points of the DRD amp. Here is distortion plot reflecting changes to the pot position.

Technical note: we obtain such sweep by running a parametric analysis in PSPICE, with the value of a global parameter P1 sweeping across a range of values. In a resistive divider, one half of the divider adds the value of P1 and the other subtracts. Thus, for the parametric sweep on R5/R10 pair from 800/2.5k to 1k/2.3k we set P1 to run from 0 to 200 by 20 and set R5 = {800 + {p1}} and R10 = {2.5k - {p1}}.

4.2   6an4 bias sweep

A change to the bias point of 6an4 results in even more interesting interplay of harmonics.

Here lower wattage corresponds to higher bias resistor values.

4.3   THDC sweet spot and load variations

What we see on the above plot is reaching of the maximum in distortion cancellation happening between the 2 stages of DRD when the biasing resistor is between 400 and 600 Ohms. Let's run distortion analysis for R3=450, for various input voltages.

Here THD is even lower, with 3rd dominating at higher volumes.

How stable is such equilibrium when other parameters change? Here is a sweep of amplifier's load.

Thus the "optimized" configuration is quite sensitive to load variations. How stable is non-optimized configuration (r3=200, r5 = 900)?

Same pattern. This data suggests that the optimum holds only for a specific load, and helps to realize that deviations in other parameters - B+, tubes - may have similar effect and help to understand that DRD must be re-tuned for desirable sonic character when tubes, load or other parameters change.

4.4   Mu sweep

For example, here is a scenario of a 300B tube gradually losing its mu or a scenario of 300b tube swapping. The plot on the right shows a sweep of 300b's Mu in range 3..4, the second plot is a family or distortion curves for mu = 3.33 (2nd harmonic sweet spot).

5.   Ultrapath connection and hum

Since Randall2 employs Ultrapath coupling to the power supply, it is fairly sensitive, according to SPICE, to ripple in power supply, see [2]. This is not a problem in Randall2 schematic because its power supply is designed with very low hum in mind. According to measurements, Randall2 produces not more than 1.5mV of hum on the output. However, if you're converting an existing SET to Ultrapath connection, and it hums noticeably at 2 * AC frequency (120 Hz in USA), and it is not a filament-induced hum (which could be determined by instantaneous disconnect of filament transformer), I suggest to get a better supply or try cancellation techniques mentioned in [2].

6.   References

[1] Plotting the results of FOURIER

[2] Hum sensitivity of Ultrapath is explained here

Author: Dmitry Nizhegorodov (dmitrynizh@hotmail.com). My other projects and articles