What types of tubes are best for use as cathode followers?

[goldear]

This is a question which I have had for a long time. Given optimum circuit implementations (in terms of biasing and load) for each given tube, are there any theoretical reason for preferring one type of 12A_7 tube over another for use as a cathode follower?

What I'm not clear about are the trade-offs involved in choosing a high-mu, high-gain tube like a 12AX7 over a medium-mu low-gain tube such as a 12AU7, or something more in-between such as a 12AT7.

It seems to me like having a lower-impedance output would be and advantage. But I'm not clear as to what makes one tube have a lower impedance than another.

Is having higher-gain and degenerating all of it via the feedback in the cathode follower with a tube like a 12AX7 advantageous, over having lower gain, and therefore not degenerating as much of the gain in a tube like a 12AU7?

I know that back in the 60s that using 12AX7s as cathode followers was common. But in the 80s and 90s it became more popular to used 12AT7s and 12AU7s. But I have no idea why that was, other than to assume that it had been learned that the 12AX7 didn't make for as good of a cathode follower.

Any insights that can be given here would be appreciated.

 

[gadget73]

Usually it has to do with plate resistance. Lower plate resistance means it can produce more current, aka lower impedance.

If you think of a tube as being a resistor between the plate and cathode connections, thats what the "plate resistance" figure actually describes. Ohm's law tells us that less resistance at a given voltage means more current flows.

 

[Tom Bavis]

Mu isn't much of a factor, as the 100% feedback in a cathode follower gives a gain of close to 1. Transconductance is important, as the higher it is, the lower the plate resistance. So 12AT7, 6CG7, 6DJ8, 12BH7, 5687 are good choices. Though in some cases, 12AX7 will be good enough, depending on what it has to drive. A preamp output that has to drive 100K and a few hundred pF of cable, may not need more than a 12AX7. A driver for a class AB2 output stage is another story.

 

[mars_volta]

12AU7 can put out more current.

 

[for_p1]

This is a question which I have had for a long time. Given optimum circuit implementations (in terms of biasing and load) for each given tube, are there any theoretical reason for preferring one type of 12A_7 tube over another for use as a cathode follower?

What I'm not clear about are the trade-offs involved in choosing a high-mu, high-gain tube like a 12AX7 over a medium-mu low-gain tube such as a 12AU7, or something more in-between such as a 12AT7.

It seems to me like having a lower-impedance output would be and advantage. But I'm not clear as to what makes one tube have a lower impedance than another.

Is having higher-gain and degenerating all of it via the feedback in the cathode follower with a tube like a 12AX7 advantageous, over having lower gain, and therefore not degenerating as much of the gain in a tube like a 12AU7?

I know that back in the 60s that using 12AX7s as cathode followers was common. But in the 80s and 90s it became more popular to used 12AT7s and 12AU7s. But I have no idea why that was, other than to assume that it had been learned that the 12AX7 didn't make for as good of a cathode follower.

Any insights that can be given here would be appreciated.

Two parameters are mostly important- Ri and idle cirrent. Also if you need to drive output stage, cathode to filament voltage limitation may come into play.

 

[dcgillespie]

Cathode followers work best when they are used to produce a low source resistance, rather than to drive a low load resistance. Hence, their popularity in the output circuits of many preamplifiers. In that application, a 12AX7 will operate as a more efficient cathode follower, because it is the inherent gain of that tube coupled with the inherent 100% NFB of the configuration that is largely responsible for the low source resistance produced. As a result, it is easy enough to have a 12AX7 represent a source resistance of under 1000 Ohms when operated as a cathode follower. So in this case, the High Mu design of the 12AX7 translates to an advantage in efficiency.

From a purely conceptual standpoint however, I agree with Tom that Mu is a low level factor, as a 12AU7 -- with less than 20% of the Mu of a 12AX7 -- can also easily enough produce a source resistance of under 1000 Ohms. It just takes more quiescent current to do so as for_p1 alluded to, because you don't have near as much gain from the tube helping to reduce the source resistance. For the general need of providing a low source resistance relative to the vacuum tube world then, both a 12AU7 and a 12AX7 can get the job done, but a 12AX7 can do so more efficiently.

All of this suggests that other than for its lower heater/cathode voltage rating, of all the common small signal triodes, the 12AT7 makes for an outstanding cathode follower, possessing both significant gain, and current handling capability (low plate resistance) to aid in producing a low source resistance.

As for which tubes were actually used most often, other factors certainly came into play as well, such as power supply design (consumption by a cathode follower relative to that of the entire circuit), inventory of tubes maintained, etc. I think as the trend became more to design with less bean counter influence, you saw other tubes besides the lowly 12AX7 pressed into CF service, because in that environment, limitations of the power supply design were greatly reduced. Of course, how bad the 12AX7 actually was in these types of applications can be debated until the cows come home!

Dave

 

[goldear]

Thanks guys! Great answers!

 

[Retrovert]

Mu isn't much of a factor, as the 100% feedback in a cathode follower gives a gain of close to 1. Transconductance is important, as the higher it is, the lower the plate resistance.

This is the key observation. I remember when I first worked all of this out, and it was surprising.

Here's a short and slightly simplified explanation.

The gain of the cathode follower (CF) roughly depends on:

(a) Tube transconductance (Gm is how effectively the grid controls cathode-to-plate current flow)
(b) The total load Impedance, RL​

The reason for this is the cathode impedance (RK) roughly varies as (1 / Gm) where Gm is expressed in mhos, not µmhos, and the tube essentially acts like a voltage divider with RK and RL.

This clearly shows that the higher the Gm, the lower the cathode impedance (RK), and the closer the tube can approach unity gain. (The CF configuration only increases current, not voltage, so the gain can be at most 1 or unity.)

For example, consider the effect of Gm on RK:

IF Gm = 500, THEN RK ≈ (1 / ( 500 * 10^-6) ≈ 2,000 Ω
IF Gm = 1,000, THEN RK ≈ (1 / ( 1,000 * 10^-6) ≈ 1,000 Ω
IF Gm = 10,000, THEN RK ≈ (1 / (10,000 * 10^-6) ≈ 100 Ω​

Which makes sense as per Ohm's Law: with a fixed voltage I = E / R, so a higher resistance reduces current and a lower resistance increases it.

Now, for the voltage divider: Vout = Vin * (RK / (RL + RK))

So the larger RL becomes relative to RK, the larger the denominator becomes and the greater the attenuation. This is why a low-impedance load is generally preferred, because as RL -> 0, the ratio approaches (RK / RK) increasing the gain.

The overall gain will be further reduced by something like (1 / µ) because that more or less accounts for the parallel resistance factor of RK, rP, and RP. But that is fortunately small.

 

[Retrovert]

The relevant characteristics for the common CF tubes are show below:

Tube GM µ
----- ----- ---
12AT7 5,500 60
12AU7 2,200 17
12AX7 1,600 100
5751 1,200 70​

So the higher Gm, but lower µ, 12AT7 will be better for a CF than the lower Gm, but higher µ, 12AX7, even taking into account the (1 / µ) reduction in gain.

(I don't know why my perfectly aligned tables have uneven formatting. They look fine when I'm editing them.)

 

[CZ4A]

6ES8/ECC189 are said to be good cathode-follower tube. They're much cheaper than 6DJ8s because the variable mu characteristic makes them undesirable for other circuits

 

[Retrovert]

6ES8/ECC189 are said to be good cathode-follower tube. They're much cheaper than 6DJ8s because the variable mu characteristic makes them undesirable for other circuits

Hmmm. I think whomever gave you this recommendation was talking about guitar amplifiers, a similar but different application, because remote or semi-remote cutoff tubes differ from sharp-cutoff tubes in ways that make them unsuitable for HiFi.

Here's a short explanation.

A remote cutoff or semi-remote cutoff (aka variable µ) tube has non-linear grid behavior than the sharp cutoff typically used. The reason is that the grid pitch (spacing between windings) is variable (typically narrow at the ends, wider in the middle), instead of constant. The looser pitch portions present a lower shielding effect than the tighter pitch regions, making it harder for lower grid voltages to drive the tube into complete cutoff. While all three types of tubes (remote, semi-remote, and sharp) operate nearly identically for large (highly negative) grid values, they function very differently for low input signal levels. The Gm is similarly affected by the cutoff characteristics, as it is derived from µ and rP.

This is somewhat simplified, but think of the grid spacing as forming a fence where the electric field around each wire controls how electrons can pass between the gap between those wires. Bigger gaps mean you need a much bigger field (i.e. higher negative voltage) in the wires on either side of that gap to prevent electrons from passing through. A smaller field narrows the gap but does not completely close it.

The remote and semi-remote tube essentially has high µ for small signals and low µ for big signals. This is very desirable in the AGC (Automatic Gain Control) section of a radio decoder so the radio can still have high gain to receive distant (weak) signals without having the front end be swamped, but have lower gain for stronger signals. Hence the AGC. Think of this as normalizing all input signals to a particular value.

Using AGC is totally undesirable in a HiFi amplifier because it is obviously non-linear. If you examine a tube chart for both types you'll see a substantial difference in behavior between 0 V and –5 V, which is the very small signals that should have a different effect. This effectively increases the µ at the low end.

Having high gain for softer portions and lower gain for louder portions would implement some sort of AVC (automatic volume control) to keep everything the same volume. That is how a compressor works, by squashing the dynamic range. This is great for guitar (so that the sound level is the same no matter how hard the strings are struck), great for CB and ham radio (so that the voice remains at a constant volume), but not so great for HiFi. Compression is also used for records to keep the needle from bouncing out of the track, and to make tiny headphones sound better (it averages the volume level so setting volume for loud passages doesn't cause soft ones to vanish, and so setting the volume for soft passages doesn't blow out the eardrums on loud passages), but it distorts the sound to do this.

Takeaway: remote and semi-remote tubes cannot be used in HiFi, which requires linearity, because of their inherently non-linear response.

 

[Retrovert]

What's more interesting, and wasn't mentioned, is how using parallel tubes can dramatically lower the noise. Switching to a parallel gain stage decreases the noise by sqrt(number of tubes). (This is true for devices in general, which is why low-signal physics experiments parallel dozens, sometimes hundreds, of devices.) So, with two tubes the noise becomes sqrt(2) or 0.707 the original noise level, or a shade under 30% lower.

 

[GordonW]

The above is correct, regarding the unsuitability of vari-mu tubes in hi-fi circuits- in the case where you're allowing the tube to actually have GAIN.

In a cathode follower- there's 100% feedback. There IS NO gain. Essentially, the cathode is at the exact same voltage as the grid, plus the bias voltage.

So, a remote-cutoff tube can work as a CF- since the 100% feedback linearizes it...

Now- if you're driving the tube to SO MUCH voltage swing that the vari-mu characteristic significantly starts to change the effective bias voltage, in a non-linear fashion- you could run into a small issue there. You'd be talking about driving dozens of volts of AC though, before this would become significant, most likely...

Regards,
Gordon.

 

[drtool]

Great thread op. Going to print this one out and study it. Thanks Wayne

 

[Retrovert]

The above is correct, regarding the unsuitability of vari-mu tubes in hi-fi circuits- in the case where you're allowing the tube to actually have GAIN.

In a cathode follower- there's 100% feedback. There IS NO gain. Essentially, the cathode is at the exact same voltage as the grid, plus the bias voltage.

So, a remote-cutoff tube can work as a CF- since the 100% feedback linearizes it...

While the gain is unity at maximum (less, of course, in practice) the tube remains an amplifier, and the Gm (how the grid affects the flow of current through the tube) is non-linear across the range, causing the cathode follower's current gain to be non-linear across the range.

The voltage doesn't increase, true, but the current flow does increase, and the grid does this in a non-linear fashion.

 

[GordonW]

If the load is resistive (primarily the CF cathode resistor)- the current can't increase independent of voltage. Ohm's law...

If you were driving a reactive load- then I'd expect some weird effects. Of course, reactive loads cause weirdness with ANY non-zero driving impedance, anyway...

Regards,
Gordon.

 

[Retrovert]

Here's the discussion of why Gm matters in a cathode follower:

------------------------------------------------------------------------
Conductance Curve Design Manual by Keats A. Pullen (1958, Reissued 2008)

[Notes on nomenclature:
eb total instantaneous plate-to-cathode voltage
ec total instantaneous grid-to-cathode voltage for triodes
es input signal voltage, instantaneous value
eg a-c component of ec
ek a-c component of cathode voltage
ep a-c component of eb
Xp plate correction factor ( Xp ~ ib/Ip ~ gm1/Gm1)
Gm1 nominal transconductance of pentode for eb/ec2 = 2 (first grid)
gm triode transconductance
gm1 transconductance, for pentode first grid (corrected)
gp plate conductance ( = 1/rp )
rp plate resistance (delta eb / delta ib, with Ec1 and Ec2 constant ~ 1 / gp )
]

The cathode follower is an amplifier ( with an amplification less than unity ) that has its output signal taken between cathode and ground. To obtain a cathode follower from Fig. 2-1, the resistance of RL is set equal to zero and the bypass capacitor across Rk2 is removed. The circuit equations then are, for the voltages:

eg = es - ek = es - ip Rk​

and

ep = -ek​

where Rk is the sum of Rk1 and Rk2. Substitution in Equation 4 gives the amplification equation:

K = ek/es = gm Rk / [ 1 + ( gm + gp ) Rk ] (11)​

The equation for the amplification of a pentode cathode follower is derived in a similar manner; using the same assumptions as made on page 8, it is:

K = gm1 Rk / ( 1 + gm1 Rk ) (12)​

and substituting for the pentode parameters:

K = Gm1 Xp Rk / ( 1 + Gm1 Xp Rk ) (13)​

------------------------------------------------------------------------​

Gm is not constant (i.e. variable) in a remote cutoff or semi-remote cutoff tube. So the gain must be variable (i.e. non-linear) across the range.

This is why remote-cutoff tubes are not used to make HiFi cathode followers, but are used in guitar amplifiers.

 

[Retrovert]

If the load is resistive (primarily the CF cathode resistor)- the current can't increase independent of voltage. Ohm's law...
If you were driving a reactive load- then I'd expect some weird effects. Of course, reactive loads cause weirdness with ANY non-zero driving impedance, anyway....

Ahhhhh, but the current does vary because the tube's resistance varies!

Remember, the internal resistance of the tube is not constant because it depends on how the grid controls the flow of electrons from cathode to plate. And what is current flow but another name for resistance? So the resistance of the tube fluctuates which means the current flow fluctuates, which means it has variable current gain. Or you can say that the current fluctuates which means the resistance fluctuates.

Voltage in a cathode follower is constant, so as per Ohm's Law, if E is constant than IR must also be constant. This means that if I increases then R must decrease, and if I decreases then R must increase. Or, the other way around, if R increases then I must decrease, and if R decreases then I must increase.

Yes, the relationship is lockstep. The assumption that both R and I are constant isn't true when the cutoff isn't linear.

Tube resistance is actually a sort of shorthand fiction. This is why, as I described above, the cathode impedance Rk varies with Gm. It's all about current flow.

 

[CZ4A]

Thanks for the explanation! I know the variable-mu characteristic is not good for hi-fi, but I didn't know that extended to cathode-follower circuits.

 

[Retrovert]

Thanks for the explanation! I know the variable-mu characteristic is not good for hi-fi, but I didn't know that extended to cathode-follower circuits.

You're welcome.

I often wonder if anyone reads these technical explanations of how tubes (or other circuits) work, or if they're too detailed.