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Old 2nd Jun 2020, 1:53 pm   #1
regenfreak
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Default VHF Miller effect, apparent inductance and LC resonance

Forgive me, i have a hard time understanding the maths about Miller effect in the Wiki page.

I have seen this explanation from an audio perspective:

http://www.r-type.org/articles/art-129h.htm

I am not interested in advanced mathematical theory but more in the practice implication of Miller effect on the resonance frequency for a LC tank in a FM/VHF receiver. My questions are:

(1) To what extent, the resonance frequency is affected by the apparent inductance of the IF transformer and the plate capacitance of the pentode IF valve at FM frequency?

The apparent inductance is caused by the distributed capacitance of the IF transformer windings. I have seen some equations in Terman.

The reason why i ask such an odd question is that I measure the L of a scrap FM IF transformer with a DER DE-5000 LRC meter at 100kHz , for example, I obtained L=12microH and C=10pF. Using LC resonance equation, f = 14.529MHz; much higher than 11.7MHz

I believe the IF transformer was correctly aligned around 11.7Mhz, so my guess Miller capacitance and apparent inductance have significant effect on the LC resonance frequency at VHF but not at MW.

(2) How signifcant does the grid to cathode capacitance of a triode affect the resonance frequency for the RF and oscillator LC tank circuits? Assume a VHF triode is used.

I have seen a triode is being used as a AFC reactance valve using Miller Effect that changes the oscillator frequency in VHF radios.
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Old 2nd Jun 2020, 2:04 pm   #2
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Default Re: VHF Miller effect, apparent inductance and LC resonance

Add the anode capacitance (e.g: 5.1pF for an EF89) plus stray C etc, say 3pF and the resonant frequency is now more like it.

Lawrence.
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Old 2nd Jun 2020, 2:34 pm   #3
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Default Re: VHF Miller effect, apparent inductance and LC resonance

So imagine you're the bit of circuitry looking into the grid of a triode. You have some value of source resistance, being the preceding stage.

You see the grid-cathode capacitance as a simple capacitor to ground (assuming the cathode resistor is fully decoupled) Easy.

You see the grid-anode capacitance, but this is not so easy. The anode isn't decoupled to ground. Worse still, the anode voltage shoots off in the opposite direction to the way you are driving the grid. Even worse, it shoots off gain times as far as you drove the grid.

Say a valve is set up to give a gain of 10 just as a convenient number.

You drive the grid 1v more positive with your signal. The anode voltage falls 10v (gain of ten inverting, remember) so the coltage on the grid-anode capacitance changes by 11 volts So the current and charge it took to get there is 11 times as much as if the same capacitance had gone to ground.

This is the current that a capacitor to ground would have taken if it had been eleven times the value of Cag. So the anode-grid capacitor is looking to you eleven times bigger than the valve data sheet quotes. This is one of the consequences of the Miller Effect.

So if I look at the total capacitance the valve presents at the grid, a large part of it is gain dependent. If I move the grid bias voltage around, I vary Gm and so I vary the gain.... and the gain varies the total capacitance seen at the grid

So I can use it as a voltage controlled capacitor... useful for applying AFC to an oscillator.

The magnified capacitance can be seen to a much smaller effect at the anode, but tuning this way would be much weaker. OK if that's what you want.

By applying capacitors and resistors to amplifiers you can simulate inductors. Even wilder, you can simulate NEGATIVE resistors. THis latter is one of the routes into understanding the modes some parasitic oscillations run in. But these areas do need maths to simplify them.

And a cascode amplifier works because the anode of the bottom valve is almost an RF ground, with very little voltage gain. Miller doesn't happen. And the top valve has its grid at RF ground, so no full Miller here.

David
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Old 2nd Jun 2020, 4:46 pm   #4
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Default Re: VHF Miller effect, apparent inductance and LC resonance

Thanks Lawrence and David

Quote:
Add the anode capacitance (e.g: 5.1pF for an EF89) plus stray C etc, say 3pF and the resonant frequency is now more like it.
That works out well.

Let La be the apparent inductance; L is measured inductance well below its self resonance frequency:

La/L = (C +Cs)/C=(10+3)/10=1.3

So La = 15.6 microH versus L = 12 microH

Quote:
You see the grid-cathode capacitance as a simple capacitor to ground (assuming the cathode resistor is fully decoupled) Easy.

You see the grid-anode capacitance, but this is not so easy. The anode isn't decoupled to ground. Worse still, the anode voltage shoots off in the opposite direction to the way you are driving the grid. Even worse, it shoots off gain times as far as you drove the grid.

Say a valve is set up to give a gain of 10 just as a convenient number.

You drive the grid 1v more positive with your signal. The anode voltage falls 10v (gain of ten inverting, remember) so the coltage on the grid-anode capacitance changes by 11 volts So the current and charge it took to get there is 11 times as much as if the same capacitance had gone to ground.

This is the current that a capacitor to ground would have taken if it had been eleven times the value of Cag. So the anode-grid capacitor is looking to you eleven times bigger than the valve data sheet quotes. This is one of the consequences of the Miller Effect.

So if I look at the total capacitance the valve presents at the grid, a large part of it is gain dependent. If I move the grid bias voltage around, I vary Gm and so I vary the gain.... and the gain varies the total capacitance seen at the grid
You articulated so beautifully that I understand the concept now. Thanks

Quote:
The magnified capacitance can be seen to a much smaller effect at the anode, but tuning this way would be much weaker. OK if that's what you want.
I will try to find an example of it. Miller effect triode AFC is not so common. Most AFC consists of a RC network across the anode and cathode of a pentode by introducing some voltage phase shift.

In addition, I have noted asymmetry of some FM IF transformers for valve radios; the capacitance is twice the value of one end (22pf vesus 10fp) , meaning that the corresponding inductance ratio is half. I do not know which is the front end. I guess it alters the L/C ratios or Q for the input/output IF tanks. What is the explanation?

Most AM IF transformers for valve radios are symmetric (L,C are identical for input and output).
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Old 2nd Jun 2020, 10:44 pm   #5
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Default Re: VHF Miller effect, apparent inductance and LC resonance

Say your triode doesn't make enough miller capacitance for your application.

Easy!

You can just add an off the shelf capacitor component from grid to anode, and the valve will multiply its capacitance by its gain. So you can make quite large variable capacitances this way.

Now a pentode has multiple grids between the control grid and the anode. These shield the grid from capacitance coupling from the anode. So they start with very low Cga, but what there is, gets multiplied by the gain as the Miller effect. As above, this can be enhanced by fitting a capacitor from g1 to anode, and the maguic of multiplication happens again. You don't need to use a triode, and you get the advantage (if you want it) of the pentode's higher gain.

Anyway, once you see the business of the capacitor not being to ground, but to an inverted and gained-up version of the signal, you're home and dry and you can figure out all the other variants that crop up.

On the principle of know thine enemy, this also tools you up on the methods of dodging the Miller effect to get better gain/bandwidth.

The miller effect goes on in transistors as well. Pretty much the same mechanism, but with a very nasty twist

The collector/base capacitance is a reverse biased diode junction, and as the voltage across it varies, so does the width of the depletion region, whch acts as the dielectric of the capacitance.... so Ccb is non-linear. Yikes! AND it gets multiplied up by the Miller effect. So non-linear Ccb gives a non linear effect to the Miller effect. Intermodulation distortion, here we come!

If doing very low distortion design with semiconductors, you really need to know the countermeasures for this. There are some and they work well. Good transistor designs can be done, but there are traps for the unwary.

David

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Old 3rd Jun 2020, 12:50 am   #6
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Default Re: VHF Miller effect, apparent inductance and LC resonance

Thanks again for the enlightenment.

Quote:
Anyway, once you see the business of the capacitor not being to ground, but to an inverted and gained-up version of the signal, you're home and dry and you can figure out all the other variants that crop up.
I must admit I have to read your sentence several times before it slowly sinks in

Quote:
he collector/base capacitance is a reverse biased diode junction, and as the voltage across it varies, so does the width of the depletion region, whch acts as the dielectric of the capacitance.... so Ccb is non-linear. Yikes! AND it gets multiplied up by the Miller effect. So non-linear Ccb gives a non linear effect to the Miller effect. Intermodulation distortion, here we come!
Before today, I never heard of Casode Amplifier that you mentioned. In the video below by w2aew, I sort of understand what he said about Casode + Miller effect and his frequency sweep demo. Once again I am handicapped by my fuzzy and inadequate understanding in the basics of trannies, as I spend 99% of the time restoring and building valve receivers. My technological mind frame is still stuck in 1940-50s. I don't have time to progress to solid state yet as it would mean lots of reading and circuit experiments:

https://www.youtube.com/watch?v=Op_I3Ke7px0

I think the Quad FM tuner uses Miller effect reactance triode (half of 12AX7) to correct the 12AT7 oscillator. I purchased the schematic from this web site so I guess I am not supposed to publish it. I never own the Quad FM tuner and I read the instruction book out of curiosity (what a nerd!).
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Old 3rd Jun 2020, 8:21 am   #7
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Default Re: VHF Miller effect, apparent inductance and LC resonance

The cascode circuit is also used with valves.

Triodes are less noisy than tetrodes and pentodes. This isn't too important on the AM broadcast bands and shortwave because atmospheric noises dominate.

But once you get to VHF and above, you want to get your receiver noise figure as low as you can. So triodes start to look very attractive if you have to use valves. Transistors can do better, but that didn't help designers before the low noise transistors became available, or if you want to use valves just for fun.

The problem with triodes is that Cga and the Miller effect severely reduce the gain at such high frequencies.

Enter the cascode circuit....

This clever arrangement dodges the problem of the Miller effect, and still leaves you the noise advantage of the triode. It is a two stage amplifier. The first stage is a normal grounded cathode stage and gives a high input impedance. The second stage is a grounded grid stage which has a very low input impedance and a high output impedance. The very low input impedance means that the anode voltage on the first stage doesn't show much voltage gain at all... it can even show loss so the Miller effect is reduced dramatically. So the first stage has no voltage gain... but we want voltage gain! That's OK, the second stage, the grounded grid provides our voltage gain. and because its grid is hard-decoupled to ground, Cga is just a capacitive load on the anode, it isn't able to do the far more damaging Miller effect. But grounded grid stages have a current gain of only one, and we want plenty of current gain.... That's also OK because the first stage gives us our current gain. There is one more bit of elegance to this brilliant piece of circuitry, by stacking the two valves you partition the HT between them and share the same anode current.

You don't have to cascode triodes, you can mix triodes and pentodes, cascode pentodes if you have to, but I don't see any advantages.

It really helps with bipolar transistors, and you can stack bipolars on top of FETs. One advantage is that you can use high voltage transistors stacked on top of high performance but low voltage devices. I used this trick pretty extensively in the hifi amplifier I designed. All the voltage amplification stages in it are cascoded. they are also differential long-tailed pairs, and are duplicated in PNP and NPN form (A trick you can't do at all with valves)

At high UHF going into microwaves, the inductance of the connection from the lower valve anode to the cathode of the top one, as well as the inductance of the top one's grid decoupling become limitations, and designeds resort to just grounded grid stages alone. There are special triodes made for this with ultra-low inductance planar grid connections.

So, dodging Mr Miller's nightmare opens up a whole world of design tricks.

Fun, in other words.

David
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Old 3rd Jun 2020, 4:49 pm   #8
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Default Re: VHF Miller effect, apparent inductance and LC resonance

Thanks David again

Quote:
This clever arrangement dodges the problem of the Miller effect, and still leaves you the noise advantage of the triode. It is a two stage amplifier. The first stage is a normal grounded cathode stage and gives a high input impedance. The second stage is a grounded grid stage which has a very low input impedance and a high output impedance. The very low input impedance means that the anode voltage on the first stage doesn't show much voltage gain at all... it can even show loss so the Miller effect is reduced dramatically. So the first stage has no voltage gain... but we want voltage gain! That's OK, the second stage, the grounded grid provides our voltage gain. and because its grid is hard-decoupled to ground, Cga is just a capacitive load on the anode, it isn't able to do the far more damaging Miller effect. But grounded grid stages have a current gain of only one, and we want plenty of current gain.... That's also OK because the first stage gives us our current gain. There is one more bit of elegance to this brilliant piece of circuitry, by stacking the two valves you partition the HT between them and share the same anode current.
I have found this paper on the design of Cascode AF valve Amp that shows the equivalent triode equation 2 :

https://www.keith-snook.info/wireles...ode%20pair.pdf

I have not got time to read it yet.


I am try to a get an idea of the order of magnitude for Miller effect input capacitance. Taking 6C4 and ECC85 VHF valve examples;


6C4: Cin = Cgk + Cgp*(A+1) = 1.8+1.4(19.5+1) = 30.5pF

ECC85: Cin = Cg(k+f+s) + Cag (A+1) = 3 + 1.5(57+1)=90pF

Correct me if I am wrong, these are very high for VHF valves. I am surprised! I assume Cg(k+f+s) to be the grid to cathod capacitance.
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Old 3rd Jun 2020, 5:25 pm   #9
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Default Re: VHF Miller effect, apparent inductance and LC resonance

Make sure you don't confuse the voltage gain with the valve's amplification factor.

Lawrence.
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Old 3rd Jun 2020, 5:40 pm   #10
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Default Re: VHF Miller effect, apparent inductance and LC resonance

Yes, the voltage gain figure to use is what the circuit sets it up to be. the valve's amplification factor is how much rhe gain could be if the circuit around it imposed no limitations.

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Old 3rd Jun 2020, 5:59 pm   #11
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Default Re: VHF Miller effect, apparent inductance and LC resonance

Quote:
Originally Posted by regenfreak View Post
I am try to a get an idea of the order of magnitude for Miller effect input capacitance...

ECC85: Cin = Cg(k+f+s) + Cag (A+1) = 3 + 1.5(57+1)=90pF

Correct me if I am wrong, these are very high for VHF valves. I am surprised! I assume Cg(k+f+s) to be the grid to cathod capacitance.
First, Cg(k+f+s) is capacitance between grid, and (cathode, heater, and intersection screen all strapped).

Since the cathode is RF earth (in common-cathode configuration), the screen is earthed, and the heater is also RF earth, this makes a useful capacitance to include on a data sheet.

Next, the formula you give is correct IF the voltage gain is 57 times. In practice, it won't be. The 57 is the maximum possible gain, with infinite load resistance (eg a constant-current load). Even if you were to use this valve as an AF amplifier, a stage gain of 30 would be more likely - in which case, replace the 57 by 30 in your calculation, giving Cin = 49.5pF.

At RF, you're unlikely to get a gain of 30 and a gain of 10 is more realistic. Now we get Cin = 19.5pF. However, at RF the load is unlikely to be a pure resistance - it's more likely to be capacitive (in which case the Miller effect makes the input look like Cg(k+f+s) in parallel with a resistance) or inductive (in which case it will look like Cg(k+f+s) in parallel with a negative resistance)

But if you use the ECC85 as a cascade, which gives the benefits that David Radio Wrangler has indicated, it turns out that the gain is around 1 from grid to anode (the anode being fed into the cathode of the second stage which looks pretty much resistive) and Cin is now 6pF.

And that is much more like what we want from an RF amplifier!

Last edited by kalee20; 3rd Jun 2020 at 6:01 pm. Reason: Punctuation
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Old 3rd Jun 2020, 6:24 pm   #12
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Default Re: VHF Miller effect, apparent inductance and LC resonance

Quote:
Yes, the voltage gain figure to use is what the circuit sets it up to be. the valve's amplification factor is how much rhe gain could be if the circuit around it imposed no limitations.
Thanks Lawrence, David, I did confuse voltage gain (stage gain A = Vout/Vin) with the amplification factor (mu) and this explains why the above figures way too high. I was scratching my head before i saw your posts. Now it makes sense

Having said that, the Cin = 151pF for the audio valve 12AX7:

https://www.aikenamps.com/index.php/...er-capacitance
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Old 3rd Jun 2020, 6:28 pm   #13
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Default Re: VHF Miller effect, apparent inductance and LC resonance

Quote:
irst, Cg(k+f+s) is capacitance between grid, and (cathode, heater, and intersection screen all strapped).

Since the cathode is RF earth (in common-cathode configuration), the screen is earthed, and the heater is also RF earth, this makes a useful capacitance to include on a data sheet.

Next, the formula you give is correct IF the voltage gain is 57 times. In practice, it won't be. The 57 is the maximum possible gain, with infinite load resistance (eg a constant-current load). Even if you were to use this valve as an AF amplifier, a stage gain of 30 would be more likely - in which case, replace the 57 by 30 in your calculation, giving Cin = 49.5pF.

At RF, you're unlikely to get a gain of 30 and a gain of 10 is more realistic. Now we get Cin = 19.5pF. However, at RF the load is unlikely to be a pure resistance - it's more likely to be capacitive (in which case the Miller effect makes the input look like Cg(k+f+s) in parallel with a resistance) or inductive (in which case it will look like Cg(k+f+s) in parallel with a negative resistance)
Thanks!! This is very helpful. Now it is clear to me. I was quite confused.
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Old 3rd Jun 2020, 6:41 pm   #14
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Default Re: VHF Miller effect, apparent inductance and LC resonance

The addition of Cin = 19.pF seems still high for a parallel LC resonance tank oscillating at 108MHz, could the actual voltage gain is much lower at FM front end?

Quote:
However, at RF the load is unlikely to be a pure resistance - it's more likely to be capacitive (in which case the Miller effect makes the input look like Cg(k+f+s) in parallel with a resistance) or inductive (in which case it will look like Cg(k+f+s) in parallel with a negative resistance)
This is a bit harder to grasp intuitively.
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Old 3rd Jun 2020, 7:30 pm   #15
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Default Re: VHF Miller effect, apparent inductance and LC resonance

It is harder, yes.

Try this: Consider a capacitive anode load. Jerk up the grid by 1 volt and hold it steady.

Then, the anode current will immediately increase. Because the load is capacitive, the anode voltage will steadily ramp downwards.

So, Cga has a steadily ramping voltage across it (grid steady at +1V, anode ramping downwards). With a ramping voltage across this capacitance, a steady current will flow through Cga.

This current must flow out of the grid lead. Now, see what we have: A steady voltage change on the grid, and a steady current flowing at the grid. That is exactly what a resistor would do, so the grid 'looks' like a resistor. (The Cg(k+f+s) is still there, so it actually looks like this fictional resistor in series with this capacitance).

It's a bit harder to visualise the effect of an inductor. However, if you remember that an inductor gives a phase shift opposite to what a capacitor does, and a capacitive load gives current on one polarity through Cga, then an inductive load will give current of opposite polarity through Cga - so input looks like a negative resistance.
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Old 3rd Jun 2020, 8:12 pm   #16
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Default Re: VHF Miller effect, apparent inductance and LC resonance

Thanks! It has started to sink in.
I can visualize your explanation better with this attachment figure taken from valvewizard.co.uk:

http://www.valvewizard.co.uk/Common_Gain_Stage.pdf

I suppose you referred to the grid leak current.

I can see what you mean by negative resistance with inductive load due to phase shift.
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Old 3rd Jun 2020, 10:11 pm   #17
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Default Re: VHF Miller effect, apparent inductance and LC resonance

Yes, but it's misleading. There is only one Cga, and the voltage across it is (gain+1) times the signal input. What he's shown has the bracketed term multiplied out and pasted on the circuit diagram, mathematically the same, but likely to cause confusion.

David
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