-3dB frequency calculation

[Steve_Bell]

In the sample circuit diagram, to calculate the -3dB roll-off frequency of signal input to the EL84, do I use the 0.22u cap and the 470K resistor, 1/(2*pi*470000*0.22E-6), or do I need to take into account the preceding stage anode resistor? That is the parallel resistance of 27K and 470K and the 0.22u cap: 1/(2*pi*[470000||27000]*0.22E-6)

[jimmc101]

The 27k resistor is effectively in series with the 470k resistor, so the calculation should be 1/(2*pi*(27000+470000)*0.22E-6).

To be exact the output impedance of the ECC83 should be taken into account, it is effectively in parallel with the 27k (in the absence of feedback this would be equal to ra which is about 45k for Ia = 2ma). See http://www.r-type.org/pdfs/ecc83.pdf

Jim

[Steve_Bell]

Isn't the HT2 rail a virtual earth to AC signals? The reason I ask is entirely economical: can I get away with using 100n caps, which I have in stock, instead of 220n, which I would have to buy?

[Skywave]

Originally Posted by jimmc101

The 27k resistor is effectively in series with the 470k resistor, so the calculation should be 1/(2*pi*(27000+470000)*0.22E-6).

Jim

Is it, though?

The ECC83 can be considered as a voltage-generator with an internal resistance of Ra, (anode a.c. resistance) which, in turn, is in parallel with the 27k, since the "HT end" of it is at a.c. ground, (or should be!) The resultant voltage which appears across this parallel combination is thus applied to the series circuit of the 220n and the 470-k. Provided that the ECC83 can produce sufficient and constant a.c. current through the 27k and the series-connected 220n and 470-k at all frequencies, the voltage across the series connection of the 220n and 470-k will be constant, (ignoring stray reactances). Ipso, the 27k doesn't feature in the calculation of the -3dB point.
When the voltage across the 470-k is 0.707 of the voltage across the 22k, this voltage will correspond to the -3dB point.

Have I missed something there?

Al. / Skywave.

[Steve_Bell]

As the ECC83 is the driving source and, subject to it's output impedance, combined with 27K anode resistor, being so much lower than the next stage, does not need (realistically) to be taken into account. Thus the -3dB point is dependant on the 220n cap and 470K resistor. Is this a reasonable assumption?

Steve.

[MichaelR]

Yes , I agree with Al , (well put by the way).

Consider the capacitor and resistor combination as a voltage divider ( calculated vectorially). Eg/Ei ratio =0.707 which is the voltage drop due to the capacitor ( Eg is valve2 grid input voltage and Ei is valve 1 output voltage).

Xc=Rg , reactance of the capacitor will equal the resistor value @ the 3db point .

Regards
Mike

[Dickie]

I agree with Al also. Whether you could hear the difference between 100n and 220n would be interesting. You could always experiment with a 100n to start with and then add another one in parallel.

[jimmc101]

Sorry I shouldn't post when I'm tired, I left out the explanation.
Remove the capacitor and look at what either end 'sees' the right hand end sees 470k to ground and the left hand end sees 27k to HT (which is signal ground) so the total resistance is 27k + 470k.

I agree the the practical effect of the 27k is small but as I said the exact -3dB calculation should take it into account.

To illustrate the point remove the 27k and ECC83, and consider a low impedance signal generator feeding the left hand side of the capacitor via a second 470k resistor. Since the input of the EL84 may be assumed to be infinite, the current through each of the 470k resistors is identical and hence we have effectively a series circuit of 470k, 220nF, 470k and this is what determines the -3dB point. Of course the drive to the EL84 is the voltage across only one resistor, but this has no effect on the -3dB point.

Jim

[Dickie]

The ratio we're talking about is 470K/(470K+27K+1/2*pi*f*C), so that makes everyone about right?

[G8HQP Dave]

You can't ignore the anode impedance of the ECC83, unless you only want a rough approximation. The exact calculation is 470K/(470K+26K||Ra+j/(2*pi*f*C)), where 27K||Ra is the parallel combination of ECC83 anode impedance Ra and 27K anode load resistor (i.e. 27KxRa/(27K+Ra) ) and the 'j' reminds us that the capacitive reactance is quadrature to resistance so we actually need to calculate sqrt(resistances^2+reactances^2).

It turns out that the error in ignoring Ra or the 27K is probably smaller than the capacitor tolerance (10%?). However, it's nice to know how to do it properly for those times when it matters. jimcc101's first post is right - everyone since then is offering an approximation.

[kalee20]

I'd agree with G8HQP Dave.

The 27k is effectively in parallel with the ECC83's anode resistance, thus giving an output resistance for the stage of around 18k (27k in parallel with ra of 45k). Add this to the 470k giving a total resistance of about 488k. Use this for the calculation of 3db frequency.

Basically, yes the 27k does feature in the calculation of 3db cut-off frequency, but as you can see its effect is highly diluted!

[dominicbeesley]

Out of interest how does one (properly) calculate the other 3db point formed by the 6k8 snubber and the el84's input capacitance? I usually have a guess at this and it usually comes out about right when I measure it...

My guess is that one can ignore the 220n altogether and and use 18k||470k + 6k8 = (24k) giving 659kHz (assuming 10pF input capacitance).

Or is it something else?

Dom

[kalee20]

Hi Dom,

Well yes in theory, you are bang on, according to the circuit diagram.

Unfortunately, in practice, it's going to be somewhat lower than 659kHz. The 220nF capacitor may have significant stray capacitance to 0V, probably another 10pF. Because this is at the left-hand end of the 6.8kΩ resistor, you'll now have a 2-pole roll-off and it gets complicated! The moral is, don't press the 220nF closely against the metal chassis, so keeping the strays negligible.

[MichaelR]

Personaly, if you read Al's statement which is specific enough to rule out the need to consider the 27K , he is also detailed enough to reason why , I think it is wrong to infer he is incorrect.

If you really want to be pedantic then you must state that every stage preceding the double triode has a wider bandwidth as far as freq response than we are are considering for this last R/C coupling.The assumption being that the OP is considering the overall frequency response.

I am raising the point not to be critical but to get understanding

For instance are you saying that at the 3db point Xc =Rg is wrong

Mike

[jimmc101]

Sorry Michael I disagree.

Originally Posted by Skywave

Provided that the ECC83 can produce sufficient and constant a.c. current through the 27k and the series-connected 220n and 470-k at all frequencies, the voltage across the series connection of the 220n and 470-k will be constant, (ignoring stray reactances).

Al. / Skywave.

Since the impedance of the 220n, 470k combination varies with frequency the loading on the 27k will not be constant and hence the voltage across it will not be constant.
Take the limit cases...
at dc Xc = infinity, voltage = ia x 27k
at high frequency Xc = 0, voltage = ia x (27k//470k)
The effect of this is to slightly raise the output at low frequencies and hence lower the roll off frequency.

I agree with Dave that the effect is small but that it is important to understand the theory.

Jim

[Skywave]

I'm beginning to wish I hadn't started this!

However, let's just re-track a bit, please.
The original statement from jimmc101 was "the 27k is effectively in series with the 470k". It was this bit that had me puzzled - and still does - & it was that particular statement that motivated me to present my analysis - be that analysis right or wrong. Moreover, I was also working on the basis that the "-3 dB point" is that freq. when the voltage across the 470k grid leak is 0.707 times the voltage across the 27k anode load.

Al.

[MichaelR]

Originally Posted by jimmc101

Sorry Michael I disagree.

Since the impedance of the 220n, 470k combination varies with frequency the loading on the 27k will not be constant and hence the voltage across it will not be constant.
Take the limit cases...
at dc Xc = infinity, voltage = ia x 27k
at high frequency Xc = 0, voltage = ia x (27k//470k)
The effect of this is to slightly raise the output at low frequencies and hence lower the roll off frequency.

I agree with Dave that the effect is small but that it is important to understand the theory.

Jim

Jim your initial statement said that the 27K was in series with 220n and 470K. Al stated that the 27K can be ignored and gave good reason why which you have also shown.His words with regard to constant voltage , I personaly read (as I am sure intended) in that the anode impedance and load CAN be ignored in this case

I agree about detail and understanding BUT the 27K is not in series with the 470K

Mike

[G8HQP Dave]

The 27K||Ra is in series with the 470K. Start at the 83 anode. You can treat this as a voltage generator with a series resistance Ra or a current generator with a parallel resistance Ra. Then add the 27K to signal ground. This either forms a potential divider with the series Ra or diverts some current from the parallel Ra. In either case you can calculate the equivalent voltage generator, which now has a series resistance of 27K||Ra. (You could alternatively just stick with the current generator, but as the rest of the circuit is a potential divider it is easier to use voltages.)

You then have a voltage generator with a potential divider consisting of three parts:
27K||Ra, 0.22uF cap, 470K.
To get the voltage across the 470K, just put that on the top and the sum of the rest on the bottom.

The calculation of HF -3dB point using the grid stopper depends too much on strays to be accurate, but in the absence of strays it would be (27K||Ra||470K +6.8K)xC etc. so Dom is right.

[MichaelR]

Dave,

You are saying this equivalent circuit is wrong then ?

What has Dom got to do with it , It is Jimmc who says it is in series.

Mike

[Barry Lloyd]

Ok, I can't resist the temptation ...
Dave's formula is correct (except that there should be a minus sign before the j, immaterial for the present discussion).
Jim's statement that "The 27k resistor is effectively in series with the 470k resistor" is correct but has given rise to confusion because it's correct only when you give the correct interpretation to the word "effectively". The two resistors can be regarded as a single value of 497k for the purposes of caclulating the 3dB point, but not when calculating the output voltage to the valve.
Ignoring Ra and valve input capacitance and writing v for the voltage generated by the first valve, r for the 27k, R for the 470k, w for 2*pi*f; the output voltage to the second valve is vR/(r + R + 1/jwC). Thus, r adds to R only on the bottom of this quotient, not on the top.
The 27k resistor lowers the 3dB frequency by 5.7%.
Barry