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What's wrong with the capacitance multiplier - and a fix

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What's wrong with the capacitance multiplier - and a fix

Postby kt88 » September 1st, 2013, 12:05 am

Hi Guys, I've posted that yesterday at HF DIY forum, but I think it might be relevant for readers of this forum as well so I'll re-post it here:

Intro: since this post is quite long, I'd like to sum this up in a sentence. This post shows an issue with the operation of the well known capacitance multiplier under appreciable load condition, with some background and simulation result as well as measured data. A solution to the problem is presented with some more simulation + measurement data for comparison - as well as a rule of thumb for selecting the right parts for your needs. </intro>

Many PS designs use the capacitance multiplier as a LPF at the input to generate a clean DC supply for the error amplifier. The simple idea is to make a small capacitor act as a much larger capacitor by utilizing the fact the BJT follower has an output impedance which is ~hfe times lower than the impedance present at its base (and an additional re, which is usually very small and can be neglected).

However, there's one problem with this topology, which seems like many designs don't really take into account. Have a look at this simple circuit:
Image

It a basic voltage regulator, with the input from the diode bridge on the left side, a capacitance multiplier for the error-amplifier, a pass transistor (in this case a BJT, but can be an MOS), and a voltage divider at the output for setting the DC voltage. The reference isn't shown, just for simplicity. Under the conditions shown here the capacitance multiplier will work just as expected. However, once we start sourcing appreciable current at the output, the voltage across C1 will flactuate quite significantly - the exact value of the "appreciable" current will depend on the capacitance at the input of the regulator (C1). The problem with this is that the assumptions under which the capacitance multiplier model was derived, are no longer true - even though the regulator itself still holds regulation as the voltage across C1 is higher than Vout+dropout voltage. This is no longer a circuit which can be approximated by a small signal model. If you look at the voltages at the terminals of T1 under these conditions it might saturate, and might even work in reverse polarity (VCB<0V).
Here's the VCE(volts) and IC(mA's) of T1 for this circuit with a 3300uF C1, 1K+100uF LPF, and a load of 1A (the results are from pSpice with the error-amp is biased at ~10mA):
Image
As can be seen the transistor conducts in both directions, so the assumption it acts as a simple capacitance multiplier doesn't hold.

However, in some cases it can indeed be very profitable to use this circuit, and when it works as expected it improves performance significantly. This issue is actually quite easy to fix with the addition of 2 parts:
Image

The addition of D1 and C4 solves the problem. Under no load it just adds an additional diode drop to the dropout voltage of the regulator (so it would be best to use a low Vf diode like a schottky diode to minimize this effect). However, under high load condition where the voltage over C1 changes significantly, correct selection of C4 will prevent reverse polarity of the transistor, and will allow the capacitance multiplier to act as we assume it acts. The correct value should be selected according the the line frequency (50Hz/60Hz) and according to the current the error-amplifier draws. The transistor T1 can operate in the forward region with VCE>0.2V, so we can allow ~0.5V of droop over C4. For instance in this example with a 50Hz input (100Hz after rectification), and 10mA in the error-amp we'll need C=I/(2*Frequency*0.5)=I/Frequency=0.01/50=200uF. Obviously using a higher value of capacitance won't hurt.
Here's the same simulation with these parts added to the circuit:
Image
As you can see, the transistor now acts exactly as we'd expect it would, which would of course improve regulation significantly.

I've also measured that on the PS I use for my headphone amplifier, so I'll be able to post some measurement data. The test was done with the only regulator I own that uses a capacitance multiplier - the output voltage was set to 24V (23.3V) with a load of ~1A (15R+8R 50W resistors in series). Measurement was done with tangent's LNMP -> Agilent U1253A (recently calibrated). This measures from 5Hz-100KHz (-3dB), and scope images were taken with the DS1052E. I'd rather not state the regulator I've used because it was designed by another member, and because this issue would be identical for all regulators that use this scheme, so the exact model is of little importance. Here are the results:
regulator with no modification:
Output noise: no load - 11uVRMS 1A load - 107uVRMS
Here's VCE of Q1 under these conditions:
No load:
Image
1A load:
Image
Indeed VCE is consistent with the simulation results with a significant AC component, and goes all the way down to 0V which means the capacitance multiplier isn't operating as expected.

regulator with proposed modification (UF1004 diode + 330uF cap (these are the closest value I've had at the moment)):
Output noise: no load - 11uVRMS 1A load - 83uVRMS
And the VCE of Q1 under 1A load:
Image
Which again is the same as in the simulation results, making sure the transistor stays in the same mode of operation - this also yield an improvement in the output ripple due to the lower ripple in the supply voltage of the error amplifier.

I've modded my regulator to include these parts and left it that way, even though under the low current I usually use with my headphone amplifier it makes no difference. Hopefully this will be helpful for other readers as well.
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Re: What's wrong with the capacitance multiplier - and a fix

Postby amb » September 1st, 2013, 11:58 am

Interesting post. I'll have to dive into it deeper to see what you're talking about.
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Re: What's wrong with the capacitance multiplier - and a fix

Postby kt88 » September 1st, 2013, 12:01 pm

Great :)
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Re: What's wrong with the capacitance multiplier - and a fix

Postby kt88 » September 2nd, 2013, 6:17 am

I would like to point out another gain of using this circuit with the modification, which might not be visible at first sight. Even though the dropout of the regulator is increased by another diode drop for a DC input, this isn't the case in real world situation. Since in practice the input voltage (across C1) will drop significantly between charges from the rectifier, this circuit modification will actually allow the voltage across C1 to drop lower without affecting regulation. Since we can now allow the minimum voltage across C1 to be lower, a lower margin above the dropout voltage will suffice.

The reason for that is the following:
The limiting factor of the dropout voltage in most designs is the path from the output to the filter cap (C1) through the control node of the pass transistor (base-emitter drop of T2 in the schematics above), through the error-amp (minimum difference between VCC and the output voltage of the error amp), through the input filter to the supply of the error-amp (the capacitance multiplier in this case). The voltage across C1 must remain above the output voltage + the minimum required voltage for correct operation of this path during the entire cycle.

In the presented circuit (with D1/C4 included), this limitation is lifted. The voltage across C1 can drop significantly lower (down to VCEsat above the output voltage in this case, and down to Vdsat above the output voltage for an MOS pass-transistor), and the voltage across C4 will still remain within 0.5V+diode drop below the maximum voltage attainable across C1 (which is usually secondary voltage of the transformer*1.4 - 2 diode drops).

I did some simulations to verify this, and with the same circuits I've used for simulations in the first post, this raised the maximum attainable output current with a 3300uF for C1 from a value of ~1A to ~2A with an output ripple of 1mVpp. So in practice this will allow a much higher currents from the same input capacitance value.

BTW, I'm trying to explain things with as much detail as possible in the hope that even readers who don't have much knowledge of electronics will be able to understand (after all, not all of us are Ti :)).
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Re: What's wrong with the capacitance multiplier - and a fix

Postby amb » September 2nd, 2013, 1:54 pm

I found some time to do my own simulations on this, and can confirm kt88's observations. I set the PSU with a "C1" bulk cap of 3000uF, set to output 30V and applied a load current of 2A. The AC mains frequency is 60Hz (therefore ripple is 120Hz after full wave rectification). The proposed fix is effective.

In the original circuit, the "problem" occurs only at sustained high current draw situations that makes the C1 bulk cap discharge significantly, before the next rectified AC pulse to recharge it again. The sawtooth pre-regulated voltage can in part dip below the voltage at C2, making the capacitance multiplier "turn off" briefly at AC mains frequency intervals. The voltage at the output rails, however, is mostly unaffected by this -- it remains steady with low ripple, albeit not as low as when the load current is lower. The fluctuations under my test load is still in the several tens of uV range.

This phenomenon does not occur in applications where there is no rectification and bulk capacitor before the cap multiplier. Hence, it does not apply to all uses of a capacitance multiplier. For example, the cap multipliers on the M³ and β22 amps' supply rails are not affected, because they are already being fed with regulated, "clean" DC.

The σ11 and σ22 however, are affected by this. As I said, it seem to make little difference in the output, but I will incorporate this modification into a future revision.

In my simulation, the added "C4" capacitor only needs to be about 47uF to work effectively. I would say to use a 100uF cap is more than enough (assuming 10mA current draw from the error amp, which is the case with σ11 and σ22). Users of current-rev σ11 and σ22 boards may choose to hack this mod into their existing boards, or just leave well enough alone.

Thanks, kt88 for your work.
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Re: What's wrong with the capacitance multiplier - and a fix

Postby kt88 » September 2nd, 2013, 9:10 pm

Hi Ti,

I'm glad to see your observations are similar to mine, and even happier to hear you'll be incorporating my modification into a new revision of the excellent sigma11/22 regulators :D
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Re: What's wrong with the capacitance multiplier - and a fix

Postby joeyjojo » September 3rd, 2013, 2:28 am

Very interesting stuff.

So what is the load current regime which leads to this ripple? And do we only need to worry about "several tend of uV" in certain applications?
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Re: What's wrong with the capacitance multiplier - and a fix

Postby kt88 » September 3rd, 2013, 3:24 am

I'm basing this on simulations of the circuit I've used for simulations in the first post, which is slightly different to the sigma11 (I've used 3300uF C1, 1K + 100uF for the LPF, 10mA bias for the error amp). I've set the output to 23.3V and the input to 24VAC (so it'll be identical to the voltages I've had in the regulator I've used for measurements).

The collector current of T1 falls down to 0A at its lowest value once the load current is 0.85A, and starts dipping below 10mA (by about 10%) at a load current of 0.7A. So personally I'd go to the "trouble" of adding this circuit once the expected average current at the output will be ~0.75A or more. This is for a 50Hz input, with a 60Hz input you can push it higher by about 20% to 0.9A.

For the price of 1 diode (preferably schottky, but it isn't a must, I've used a UF1004 as it has the lowest Vf I've had) and a single 100-220uF capacitor, I don't see a reason why you shouldn't have the benefits of this modification (assuming you are using currents similar to what was stated above).
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Re: What's wrong with the capacitance multiplier - and a fix

Postby amb » September 3rd, 2013, 4:03 am

joeyjojo wrote:do we only need to worry about "several tend of uV" in certain applications?

To put things in perspective, that's only slightly higher output ripple than at little or no load conditions, and still outperforms 3-terminal IC regulators by a significant margin.

With four β22 boards (adjusted to default bias levels and used as a headphone amp), running on a single σ22, the total load current only begins to approach the threshold where this phenomenon would occur.
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Re: What's wrong with the capacitance multiplier - and a fix

Postby cobretti » September 3rd, 2013, 1:04 pm

without doing any simulations, I put this diode here as a protection for transistor Q1 when output is accidentally shorted, and I also implemented this diode into my dual LAB power supply. 8-)
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