# Ultrapath Line Stage

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

## 1.   Introduction

In this article we explore the Ultrapath topology as a candidate for line-stage amplifier. What tube to use, which parameters are the best, what are the requirements for the power supply? We'd like to get low distortion, low output impedance, large headroom, low noise and hum. We try several different tubes and use PSPICE to find the best configuration for each tube.

## 2.   6GM8/ECC86

This tube is a promising candidate because there is small audiophile cult around it and because its low-voltage, low-heating design permits use of battery power both for plate supply and for filaments, thus reducing hum to zero.

### 2.1   PAENG Model

For initial simulation, I used Stefano Perugini's (PAENG Design) model [5] that is based on Norman Koren's Improved Triode Model but adds polynomial function a2Vp^2 + a1Vp + a0 in place of Ex:

 ``` .subckt ecc86 1 2 3 ; placca griglia catodo + params: mu=14 ex=1.71 kg1=295 kp=220 kvb=100 rgi=2k + ccg=3p cgp=1.3p ccp=1.8p a2=0.0083 a1=-0.022 a0=1.1033 e1 7 0 value= +{v(1,3)/kp*log(1+exp(kp*(1/mu+v(2,3)/sqrt(kvb+v(1,3)* +v(1,3)))))} re1 7 0 1g e2 8 0 value={a2*v(1,3)*v(1,3)+a1*v(1,3)+a0} re2 8 0 1g g1 1 3 value= {(pwr(v(7),v(8))+pwrs(v(7),v(8)))/kg1} rcp 1 3 1g c1 2 3 {ccg} c2 1 2 {cgp} c3 1 3 {ccp} r1 2 5 {rgi} d3 5 3 dx .model dx d(is=1n rs=1 cjo=10pf tt=1n) .ends ```

On the plate curves below, grid lines are in .1 V increment, starting from 0. The plot looks odd and artificial because the model is polynomial:

The plot shows that it is difficult to achieve significant voltage swing here, as the max idle plate voltage can not be more than 25V. This remarkably limits grid voltage to 0.4 V in high-current region. It's also evident that this tube is model is sensitive to variations in load impedance - because its curves are so complex, which is especially true when plate current is lower than 5 mA. There is a knee in plate curves at around 4..5 mA where plate voltage is < 20V.

note on the transformer:
An output transformer for a 600 Ohm linestage commonly has a 4:1 or 5:1 ratio of turns. However, this is typical of high-voltage tube stages, and seems limiting the voltage swing of a 6GM8/ECC86 linestage too much. With >4:1 winding ratios the stage will not be able to produce more than 2VRMS before clipping. I assume a good linestage should be tuned for 1.5 VRMS as 0db out, with +8..+12db headroom to accomodate transients, which means around 5VRMS out before clipping. For this reason I suggest using a 2:1 winding ratio. This gives total amplification factor of 7. and output impedance ~ 900 Ohm. With 2 halves of each 6gm8/ecc86 tube connected in parallel it is ~ 450 ohm, which is OK for most applications. I would not use 1:1 because in this case the output impedance will be too high (~ 900 ohm, 2 tubes), but I'd consider having a tap coming directly from the plate to feed easy loads.

First set of distortion data is for 7 mA plate current, which translates to ~ .68V bias:

 Input range 10mv..1v. 2:1 winding ratio.

The cathode resistor is 90 ohms which gives the above mentioned 7ma of plate current.The load Rload for this set is 600 Ohm. Distortion curvers for other loads are fairly similar and consistent.

Harmonic ballance shifts in the region of low plate current, though, due to the above-mentioned "knee" in plate curves. Below I show some parametric swepps for this region with a disclaimer that Stefano Perugini's plynomial model does look exotic to me. However, I do believe that low-voltage low-current conditions add some complexity to plate curves that indeed may cause various sonic surprises, and the polynomial model attempts to address that.

 This data is for a 300 Ohm load, sweeping the bias resistor value in the range 250...50 Ohm. The first "column" of distortion points (left side) is for 250 Ohm, the last "column" is for 50 Ohm. Input is .1 V.

There is a peculiar local sweet spot around 200 Ohm, where the 2nd harmonic appears to be very low. Apparently, the loadline crosses the "knee", and the shape of the "knee" provides distortion cancellation for the 2nd harmonic. The optimal value is around 190 Ohm. Here is distortion data for varying input voltages with Rk = 190 Ohm:

This significantly differs from Rk=90 data, and such difference would be readily audible. Lower 2nd harmonic and higher 3rd may or may not - depending on your preferences in sonic signatures of SET amps - sound appealing, but the main issue here is that distortion patterns in this region are highly unstable. For example, if we run this configuration with 50K load, the picture is completely different:

What is the value of this analysis? Can Rk=190 Ohm be suggested as the best bias resistor value for this schematic? The answer is no. Even if the model is quite accurate, the sweet spot will position differently for different tubes. On another hand, fine-tuning the bias resistor may result in interesting but very fragile, sonic surprises, which could be a part of 6gm8/ecc86 reputation. Of course, if 6gm8/ecc86 triodes are parallelled, each must have a separate biasing.

### 2.2   Koren Improved 6GM8/ECC86 model

I see why Stefano Perugini used a polynomial model on 6gm8/ecc86: the tube curves do not mesh well with more conventional models. Still, Amperex data for 6gm8/ecc86, see [8], does not look close enough for me to SPICE plate curves above. After I wrote my interactive model parameter finder, I tried to come up with a reasonable approximation using Koren Improved model. Here is the screencapture of the app, showing model curves over Amperex's plate curves. On the left I show Koren Improved model with parameters for 6gm8/ecc86 obtained with my interactive tool.

``` .SUBCKT 6GM8 1 2 3 ; P G K ;
+ PARAMS: MU=21 EX=1.596 KG1=435  KP=46.5 KVB=24.1 VCT=0.44 RGI=2000
+ CCG=3P  CGP=1.4P CCP=1.9P
E1 7 0 VALUE={V(1,3)/KP*LOG(1+EXP(KP*(1/MU+V(2,3)/SQRT(KVB+V(1,3)*V(1,3)))))}
RE1 7 0 1G
G1 1 3 VALUE={(PWR(V(7),EX)+PWRS(V(7),EX))/KG1}
RCP 1 3 1G ; TO AVOID FLOATING NODES IN MU-FOLLOWER
C1 2 3 {CCG} ; CATHODE-GRID
C2 2 1 {CGP} ; GRID=PLATE
C3 1 3 {CCP} ; CATHODE-PLATE
D3 5 3 DX ; FOR GRID CURRENT
R1 2 5 {RGI} ; FOR GRID CURRENT
.MODEL DX D(IS=1N RS=1 CJO=10PF TT=1N)
.ENDS

```
Simulation with this model into a 100K load and a 2:1 transformer does not show a low-distortion sweetspot but instead displays monotonic increase in 2nd harmonic up to a fairly high value at ~ 4.5 VRMS, and then going down yielding to higher order products (as it always happens when severe limiting/clipping kicks in):

With 4:1 transformer the value of useable VRMS will be halved.

## 3.   6C45PI

In comparison to 6gm8/ecc86, 6c45pi (a.k.a 6c45) is a very "proper", linear tube. It has a reputation for high-frequency oscillation, though, so grid stopper resistors are a must.

With 4:1 ratio for the output transformer, 6c45pi gives around 320 Ohm of output impedance. No doubling is necessary!. 320 Ohm low enough for most applications, except for low-impedance headphones.

## 4.   6N1P, 6SN7

These tubes are good candidates for Ultrapath linestage as well, offering driving capabilities and distortion patterns similar to 6c45pi. Since these tubes have higher plate resistance but in turn accommodate higher B+ and hence deliver more voltage swing, for optimal loading the output transformer should have higher turns ratio. Ideally, a multitap, 8:4:3:2:1 transformer can be used for various loads.

## 5.   The Challenge of Ultrapath

The ULTRAPATH topology is captivating because as Jack Elliano explains, the power signal path is very short and consist of only 3 elements, the tube, the high-quality capacitor (C1) and the transformer. The path through the ground into power supply is eliminated. This is very appealing. Is there a downside? I I heard reports that ULTRAPATH is very demanding to power supply ripple. PSPICE simulation reveals that indeed, AC noise coming from the power supply is a challenge for ULTRAPATH.

I added 1 mV of 120 Hz AC to the B+ supply and ran simulation with 6n1p tube's greed to the ground. The choice of 6n1p tube for this test was for its medium amplification factor, not too low (6SN7,) not too high (6c45). The value of C1 was set to 40uF.

The Ultrapath topology developed 8 mV of AC signal on the output. If we disconnect C1 from B+ and connect it to the ground it becomes a classical bypass capacitor. In this configuration, the output AC signal is only ~ 150uV. Finally, with C1 eliminated the output AC signal is ~ 300 uV. In all three tests the AC signal on B+ is the same - 1 mV.

In other words, it appears that C1 injects AC ripple into cathode bias and lets the tube amplify it. The ratio 8 mV : 1 mV is close to the gain of the circuit (transformer's ratio is 4:1). One way to understand this is to realize that the tube can be presented works as a ground-grid amplifier here, with input signal (ripple) fed into the cathode.

This is indeed a challenge, as it appears that Ultrapath amplifiers AC ripple of power supply. This will be worse with high mu tubes such as 6c45.

## 6.   A solution

I'm a reader of John Broskie excellent tubecad webzine, and I remember the series of articles on hum cancellation [3]. I know that a signal injected into cathode circuit can cancel out the same signal on B+ if correct amount is used. This is so because the signal on the plate is an inversion of the signal on the cathode. Tube distortion and transformer imperfection and various phase shifts caused by RCL elements may add some residuals, but with proper value of injected signal cancellation will be very significant. ULTRAPATH, in some sense, injects way too much signal. Most of it needs be removed. For hum cancellation purpose Broskie provides a brilliant solution - a C/C voltage divider. It is very relevant to our topic because one of these caps in in fact the ultrapath cap C1, Hence all we need is to add a bypass cap to an ultrapath circuit! Theoretically, this can serve as the most elegant way to "fix" hum pickup in ULTRAPATH topology. John Broskie gives formulas to compute the ratio of the capacitors in the divider. That would be the end of the story, however, I found 3 practical difficulties.

First, SPICE reveals that perfect cancellation happens only if impedance of C1 is much greater than Rk. Otherwise, phase shifts occur, preventing complete cancellation. I suspect what matters here is how much impedances of C1 and the bypass cap lower than Rk. If C1 is 1uF, its impedance at 120Hz is ~ 800 Ohm - more than Rk for 6n1p, 6c45, 6gm8/ecc86. Phase shift is significant, cancellation is not full. 100uF is ~ 8 Ohm at 129 Hz. Can be used for 6n1p with OK success, but still not very good for 6c45 or 6gm8/ecc86. In fact even for 6n1p, where Rk is 500 Ohm, cancellation is not perfect due to slight phase rotation:

on this plot the first curve is for Ck = 3550uF, 2nd - 3560,....

Note that in the ultrapath circuit C1 plays the role of a bypass cap, and thus its impedance needs be lower than Rk on the low end of the range, not at 120 Hz, and hence it must be large anyways - as large as "normal bypass". Unfortunately, unlike for normal bypass, C1 must be rated for high voltage.

Second, as the bottom capacitor needs be ~ mu times bigger than C1, with large C1 it can get way too large. Thus for C1 = 100uf and for 6n1p with mu=33 we get 3300uF.

Third, tuning for zero hum is a pain because changing value of a large cap for hum adjustments is a pain. Even after someone assembles the correct value, cancellation will be prefect only for a given mu of a given tube at given point in its lifetime.

Therefore, there is a need to find another method of hum adjustment. What about a solution involving a potentiometer? After some thinking I came up with several approaches. Since I figured out that a proportion of ~ 1/mu of B+ ripple injected into cathode will cancel it out, how about injecting the whole ripple signal into a 1/mu part of the bias resistor? The exact amount is not 1/mu, and John Broskie provides formulas for that, but since I use SPICE, i need to sweep around that value. Which I did with a circuit where Rk was replaced by a parametric pair simulating a potentiometer, with one side of the ultrapath capacitor C1 attached to B+ and another to the tap of the pot. Unfortunately, no cancellation happened - the "load" was too low for C1's impedance. I saw phase shifts suggesting that. Then I switched to circuit where C1 feeds a voltage divider and was able to obtain clean cancellation. Note however, that as the result the circuit lost bypassing and therfore the gain is lower and output impedance is higher.

OK, what about injecting the signal into the grid? This will help to fine-tune either a classical bypassed stage or a stage with Broskie C:C divider (slightly unbalanced) for lowest hum:

Thus we started with ULTRAPATH, considered Broskie divider and ended up with a topology that provides hum cancellation with or without the ultrapath capacitor C1 present. How about using grid hum injection in the original ULTRAPATH topology? This appeared doable but after closer examination revealed problems, as the grid needs to see even slightly more hum than what reaches the cathode. I'll continue experimenting with this.

## 7.   Conclusions

### 7.1   Topology

The original Ultrapath topology is prone to pruduce excessive hum. The reason for that is cathode hum injection. Expect about Mu times more hum than in classical cathode bypassed topology. This hum pickup is one of the reasons Ultrapath is often associated with battery power supply.

The hum-cancellation topology presented in the last section of this article, which is in between John Broskie cancellation circuits and Jack Elliano ULTRAPATH may be a promising remedy to "tried Ultrapath, but got too much hum" syndrome. A "short audio path" is present here just lik ein the original ultrapath topology, although there are few more parts in the schematic.

### 7.2   Tube Choice

Speaking of tubes, 6gm8/ecc86 seems worth the trouble only for battery applications. Because hum and power supply noise is not an issue there, ULTRAPATH and 6gm8/ecc86 are a good match. Note that trying to tune into its distortion-cancelling region (if it exists) using a battery supply without a voltage stabilizer is pointless. Without that, though, the tube appear much less linear then 6sn7, 6n1p, 6c45.

## 8.   References

[1]. Jack Elliano Ultrapath.

[2]. John Broskie Tube Articles.

[3]. John Broskie C:C Hum Cancellation.

[4]. PAENG Design's article on High Gm, High Mu Tubes.

[5]. PAENG Design Tube Models.

[6]. Norman Koren's Improved Tube Models.

[7]. Chris Beck's 6SN7 Ultrapath.

[8] Amperex 6GM8/ECC86 data on Frank's Electron tube Pages.

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