Keep in mind,the more complicated ladder attenuator was developed long ago,when resistors were much noisier than today. [...] Cost and complexity considerations aside,my thought is that with modern,low noise tight tolerance metal film resistors,any alleged advantage of the ladder over the series attenuator will be nullified by the additional switch contact.
I thought that too, then I thought some more, and did some research into Johnson noise to refresh my faded memory.
Johnson noise in resistors works in such a way that a series of
n resistors each of value Rs has sqrt(
n) more noise than a single resistor of value (
n x Rs). Correct me if I've misunderstood this.
The magnitude of noise voltage for a resistor varies as sqrt(R x
K) where
K is some constants, temperature, etc. So we can say the noise varies as sqrt(R) since all the other factors are constant for a single vs. string. Each resistor is independent of the others in terms of noise, and its noise is a function of its resistance multipled by some other factors. But it will vary as a f(R).
So that means to compare
Rt as a single resistor vs
Rt = R1 + R2 + ... Rn resistors in a string, the maximum effect (all resistors in sequence) is going to be:
[sqrt(Rt)] vs [sqrt(R1) + sqrt(R2) + ... sqrt(Rn)]
In a series string the values are all equal, say Ri. So this reduces to:
[sqrt(Rt)] vs [n x sqrt(Ri)]
So if the string is, say 250 kΩ built from (25) 10 kΩ resistors then Rt = 250,000 and Ri = 10,000. So the noise would be:
sqrt(250,000)
vs [25 x sqrt(10,000)]
500
vs (25 x 100)
500
vs 2,500
So at the maximum value, I think the single resistor has 1/5 of the noise of the string. Noise in a string of
n resistors appears to vary as sqrt(
n).
The question is how noisy is a 1% metal film resistor. Not very. A carbon composite is very noisy.
Hafler experienced substantial resistor noise with the PAS which delayed shipment:
“An Interview with David Hafler, Part 2: The Dynaco Years” by Charles Kittleson, Vacuum Tube Valley, Issue 16
Just about the time we were ordering parts, I noticed a peculiar kind of noise coming from it when it was turned up all the way. The prototype unit didn't have the noise problem. I tried everything that I could think of for weeks, and tried to pin the problem down. I even had Stewart Hegeman come in from New York to analyze the noise problem. He took a look at it and couldn't find the answer (laughter).
I finally resolved the thing by taking the preamp apart, piece-by-piece and interchanged them between my breadboard unit and the pre-production unit. I found that the low-noise resistors were noisier than anybody could have anticipated. They were just no good. It took me all that time to find it because they were consistent. They had the same harsh, rushing, waterfall kind of noise.
That delayed shipping by several months at a time when the demand was really high. So when we started shipping, we had back orders for a couple thousand units.
