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There are some posts and discussions how a circuit popularly called a “capacitance multiplier” could reduce low frequency ripple noise (at 50/60 Hz or 100/120 Hz) and could perform better than common (jelly bean) series regulators for higher-frequency noise ripple, as 10 kHz to 100 kHz, for instance.

I presented some context and references first, then posted questions interleaved with comments to share my points of interest - in case you see shortfalls in the examples or logic, please help to clarify the matter.

Clarification: I don’t know who named the circuit a ‘capacitance multiplier’ and I agree with Tobalt that such a circuit behaves as a ‘buffered low pass’ that could be nicknamed better (as ‘ripple smoother’, etc.), but that capacitance multiplier is preserved here for its popularity, as other misnomers in electronics - ‘Joule thief’, for instance.

Classic Capacitor Multiplier and Variants:

  1. Single-resistor + capacitor on transistor-based capacitance multiplier as seen here and explained by Dave’s EEVBlog here and his video here:

enter image description here

  1. Reduced voltage with resistor-divider + capacitor feeding transistor on capacitance multiplier to increase linear operation of the transistor - discussed here and in Elliott Sound Products (ESP here) - both highlighted in yellow:

enter image description here.

enter image description here.

Update: The functional improvements of using this resistor are didactically explained by ‘FesZ Electronics’ video here with simulations in LTspice.

  1. Reduced voltage with Zener + capacitor feeding transistor - it could be seen either as a capacitance multiplier or as a crude series regulator - as seen here:

enter image description here

The right-side circuit includes some additional diodes for protection of the transistor, sure, as addressed and modeled by Antonio51 here (and in another post, but I could not find the link in this question).

Questions:

  1. Why does the capacitance multiplier have a better response ‘filtering’ the higher frequencies from Vin to Vout than a series regulator (at least for LDO as MCP1700 - upper left)?
    See, for example, the screenshots from the above mentioned EEVBlog’s video - showing ripple response at 100 Hz and 10 kHz:

enter image description here

Clarification: the author of that ‘video tutorial’ is also the administrator of EEVBlog and he is the one who compares some ripple features of a low power LDO regulator (as MCP1700) with this capacitance multiplier.

I’m just delivering/sharing the message, from a reputable (for me) source of information.

  1. Regarding noise and ripple suppression, is a capacitance multiplier circuit as good as (or better than) common (aka jelly bean) series voltage regulators?
    Please consider not only 100/120 Hz (linear PS) scenario, but also 10 kHz and 100 kHz (SMPS) as “ripple noise” fundamental frequency.

Some datasheets of common LDO regulators as AMS1117 do not post ripple rejection per frequency, but TI’s LDO LM1117 shows these curves:

LM1117 - Ripple rejection

Moreover, regular series voltage regulators as TI’s LM317 show similar response as ripple rejection of about -60dB (@ 10 kHz) reducing to -40dB (@ 100 kHz), when 5 V is available as voltage differential (Vin-Vout):

LM317 - Ripple rejection

On the other hand regarding the capacitance multiplier, the screenshots of that video show an attenuation that is not strongly dependent on the noise frequency - compare the responses at 100 Hz (lower left) and 10 kHz (upper right.)

  1. Could the above behavior be seen as “less frequency-dependent” response of the capacitance multiplier and be extended to 100 kHz or more? If not, which would be the limitations expected?
    Wouldn’t it be useful as a kind of ‘power-filter’ (or amplified RC - see screenshot at lower right) to reduce the noise generated by SMPS and ‘ringing glitches’ that some diodes and inductors/transformers could cause?

Update: Regarding high frequency (HF) noise sources and their filtration, caused by SMPS, this FesZ’s video shows both in simulation and in real life how to reduce such noise, but my point here is to understand if the capacitance multiplier would be capable of reducing the HF ripple noise and be less frequency-dependent as illustrated by EEVBlog’s video.

Disclaimer: I know the terminology I used is far from the most adequate one, so I would appreciate hearing any better definitions as answers or comments to explain such phenomena.

  1. Could the capacitance multiplier (all 3 variants shown above) be seen as an open-loop circuit of current-amplified ripple suppression?
    If this is unacceptable by any means, could someone elaborate where (and how) this ‘loop’ is ‘closed’?

I see it this way: while not being a voltage regulator, it could be loosely seen as a faster “ripple suppressor”, using the intrinsic RC response polarizing the base of the transistor, while amplifying the output current, due to hFE of the BJT.

Probably a more comprehensive model of a BJT operating at really high frequencies >> 100 kHz and its internal capacitances and inductances could change the response of the component itself (BJT.) I don’t know how this would be modeled and how much this influence would be.
Furthermore, wouldn’t this be worse on a linear regulator with error amplifier, etc., which would be really be operated in a closed-loop layout?

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    \$\begingroup\$ It's a buffered lowpass, so its PSRR is about as good as that of the lowpass..But its output impedance is rather bad compared to actual linear regulators with feedback. \$\endgroup\$
    – tobalt
    Jan 28, 2023 at 5:32
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    \$\begingroup\$ Btw, CM in context of filtering and noise is usually interpreted as common-mode. So you could consider another abbreviation, or another name. This circuit doesn't multiply capacitance. It is a buffered lowpass, nothing more, nothing less, so maybe BLP ;) In notes/discussions I call it "ripple eater", somewhat in line with your bullet (4.) \$\endgroup\$
    – tobalt
    Jan 28, 2023 at 6:51
  • \$\begingroup\$ In (1) why are you comparing the basic emitter follower (quiescent current in the several mA region and a drop-out voltage around 1 volt) with the MCP1700 (really low quiescent current of 1.6 uA and low drop-out voltage below 200 mV). The tech in the MCP1700 is massively different and fulfils a different market area entirely. The comparison is loaded and weak. \$\endgroup\$
    – Andy aka
    Jan 28, 2023 at 9:46
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    \$\begingroup\$ @tobalt, good points. I will update the Question to avoid this confusion. I’m Brazilian, so a sense of humor is always welcome (for us) to lighten things. I didn’t named it ‘Capacitance Multiplier’ as a known term and don’t know who gave such name. I agree (and Iike) your ‘Ripple Eater’ or ‘Ripple Smoother’ as making more sense to me, especially because it does not really multiply the capacitance, but works just as buffered current amplifier, as you mentioned. Other misnomers in as ‘Joule Thief’ are popular, but if you look for ‘blocking oscillator’, it has lesser popularity. \$\endgroup\$
    – EJE
    Jan 28, 2023 at 15:59
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    \$\begingroup\$ @Andyaka, who did such comparisons was not me, but Dave (administrator of EEVBlog) that is hugely more knowledgeable than me in electronics. I cannot disagree with you, but Dave has presented good points to think, as FesZ too (updated links). About the MCP1700 and CapMult comparison, if they are ‘weak’, I’m just the ‘messenger’, ok? About asking for other Voltage Regulators, ok, I’m the author of this doubts and I’m not an Electronic Engineer, just a retired Mech.Eng. with PhD in other area than EE, who is passionate about electronics. And for these doubts, I’m guilty ;-) \$\endgroup\$
    – EJE
    Jan 28, 2023 at 17:06

3 Answers 3

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1 - Why the Capacitance Multiplier has a better response ‘filtering’ the higher frequencies

The very low quiescent current of the MCP1700 suggests that \$gain \times bandwidth\$ product is not wonderful. Indeed, at 10 kHz., line regulation sucks...data sheet suggests that output ripple should be about half input ripple.
\$\beta\$ of the capacitor-multiplier at 10 kHz. is pretty-much identical to \$\beta\$ at 100 Hz. Ripple rejection of its RC filter should improve as frequency goes up, at least to a few MHz, where \$\beta\$ starts to fall off.

2 - Regarding noise and ripple suppression can a CM circuit be considered as good as (or better than) common (aka jelly bean) series voltage regulators?

Keep in mind that capacitor-multiplier filtering ripple rejection is dominated by its RC low-pass filter, so low-frequency filtering should be inferior to a properly designed active regulator. Even with \$\beta multiplication\$ a very large RC product is needed to filter low frequency ripple.
As for low-amplitude noise, many transistors (especially the physically-larger ones) have lower intrinsic noise sources than the op-amp-like gain stages inside active regulators...especially if you consider 1/f noise at really-low frequencies.
Trying to filter-out this really-low-frequency noise with a shunt capacitor attached to an active regulator's output is nearly impossible, because output impedance is often a fraction of an ohm. This output-shunt capacitor only starts to be effective when the internal gain stage of the active regulator drops-off at high frequency (perhaps above 10 kHz).
Dave mentions in his blog that ripple rejection of capacitor-multiplier circuit can be quite good, but stresses that load regulation is terrible when compared with an active regulator like LM317.
As for switching regulators, consider noise at frequencies not related to switching frequency and its harmonics. Noise floor performance in this context can be as good as linear regulators.

3 - Could the above behavior be seen as “less frequency-dependent” response of the CM and be extended to 100 KHz or more? If not, which would be the limitations expected?

Above 100kHz, a shunt capacitor adjacent to the load should be considered superior. Inductance of conductor paths between regulator and load (and back) become significant.
As for the capacitor-multiplier circuit, equivalent-series-resistance of the (electrolytic) capacitor becomes significant at some point.
Dave also misses the nasty tendency of the capacitor-multiplier circuit to oscillate at very high (VHF) or ultra-high (UHF) frequencies. Take a closer look at OP's upper-right photo of Dave's test circuit. It shows a fuzz on top of output waveform. This fuzz could possibly be oscillations at hundreds of MHz. Tiny inductances in the base and/or emitter have not been accounted for that cause oscillation. Oscillation amplitude is often small and easy to miss. In actual use, I have often found this simple capacitor-multiplier oscillating - but a good quality 'scope doesn't show it. Ferrite beads on base and/or emitter might be needed.
barely-oscillating "capacitor-multiplier"

4 - Could the CM (all 3 variants shown above) be seen as an Open-loop circuit of current-amplified ripple suppression?

Be careful here - you're assuming linear circuit operation. Consider that a down-stream capacitor often exists. This capacitor-multiplier circuit can only source current, and cannot sink current. A non-linear load can suddenly disappear, or even rise in voltage momentarily. Transistor current falls to zero.
Many active regulators suffer the same problem, but since their load regulation is often far superior to capacitor-multiplier circuit, the consequences are less-dire.


An alternative noise-reducing post-regulator circuit:
Charles Wenzel offered this feed-forward noise cancel circuit. Like a capacitor-multiplier, load regulation is not great. Unlike a capacitor-multiplier, AC noise is amplified, inverted, and current is added to output so that very low-amplitude noise is attenuated. It can improve noise performance of many linear regulators.Wenzel's noise filter

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  • \$\begingroup\$ First of all thanks for being the first one to provide an answer. I have some points to reply: Q&A1 good point regarding beta’s frequency response. Being an RC, I would expect -20dB/decade, right? Curiously on the screenshots we see 500mV ripple reduced to 2.3mV at 100Hz or to 2.6mV at 10kHz. Freq = 1/(2*pi*1K*470u) = 0.33 Hz. Wouldn’t this make -50dB attenuation at 100Hz? Then why it is about a similar reduction for 2 decades higher (10KHz)? BD135 is a NPN with f_t = 190 MHz (frankshospitalworkshop.com/electronics/data_sheets/b/BD135.pdf) so it might not be the culprit for that. \$\endgroup\$
    – EJE
    Jan 28, 2023 at 18:13
  • \$\begingroup\$ About Q&A2 - I would expect an LC or better regulator to operate at -40dB/decade, but shown LM317 and LM1117 ripple rejection curves show about -20dB/decade = about the same as an RC decay. So, although I understand your point, it is not shown in the datasheets - at least for the ‘jelly bean’ ones. Surely a regulator provides something that a CapMult doesn’t: regulate the voltage. This by itself would be the main reason to choose a regulator instead of a CapMult, unless ripple rejection is a must. I’m not a musician or guitar player, but they often complain about ripple in PS. \$\endgroup\$
    – EJE
    Jan 28, 2023 at 18:23
  • \$\begingroup\$ About A3: Ok, an Electrolytic Cap has higher ESR and ESL that for high frequencies, if used alone, would not work so well. To solve this issue, paralleling with a Ceramic cap would work, no? The point also would be that the transistor buffering/amplifying the current and following its base voltage (now HF smoothed) would work intrinsically well - or did I miss something? You did catch and comment on A3 about the ‘fuzz’, also mentioned along the EEVBlog posts. Would it be a fair statement to consider CapMult with a Ceramic cap added and a ferrite bead at Base addressing all that? \$\endgroup\$
    – EJE
    Jan 28, 2023 at 18:34
  • \$\begingroup\$ Dave's measurement @ 10kHz is perhaps careless - his 'scope's "2.6mV" ripple measurement is closer to 0.5mV from what I see from the photo. The difference is due to the fuzz (that I suspect is VHF oscillation). 0.5mV p-p is still not as low as you'd expect. A crude LTspice simulation showed 100Hz ripple = 7.9mV while 10kHz ripple was 0.198mV assuming capacitor ESR of 0.1 ohm. I used a 2N2222 model. Everything looked linear. Yes, -20dB/decade should apply for linear operation. \$\endgroup\$
    – glen_geek
    Jan 28, 2023 at 18:48
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    \$\begingroup\$ @EJE went back to LTspice and added small base inductor, and some small emitter-to-GND capacitance (see recent edit above). It is a squegging oscillator @ 300MHz where 2N2222 runs out of gain. Didn't try other inductor/capacitor combos, as this one oscillated first try. When probing a capacitor-multiplier circuit on PCB, I noticed that adding multimeter probes from emitter-to-GND caused a slight DC shift that gradually settled. Adding ferrite bead stopped the shift - my available 60MHz 'scope couldn't see the small oscillations involved. \$\endgroup\$
    – glen_geek
    Jan 28, 2023 at 19:54
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Why does the capacitance multiplier have a better response ‘filtering’ the higher frequencies from Vin to Vout than a series regulator

There is nothing intrinsic about a linear regulator that gives it poor ripple rejection. In fact many linear regulators have excellent ripple rejection, at both low and high frequecies.

What is intrinsic to linear regulators, and indeed to all engineered products, is that their design involves trade-offs.

A capacitance multiplier trades voltage headroom for ripple rejection. The ripple rejection is not "free".

If a given linear regulator has insufficient ripple rejection at a frequency of importance, AND one has sufficient voltage head-room to play with, then one can cascade a capacitance multiplier with a linear regulator, OR one can choose a different linear regulator.

On the other hand, if one's objective is to, say, provide a regulated 3.3 volt output from a Li-ion battery, that might need to operate at a terminal voltage as low as 3.6 or 3.7 V, one neither NEEDS special ripple rejection, nor can one AFFORD (in terms of loss of headroom) the superfluous ripple rejection.

In short, low drop-out may be the primary design objective of a linear regulator, or high ripple rejection may be the primary design objective, or their may be some other primary design objectives (or some compromise) but it all boils down to design objectives.

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  • \$\begingroup\$ Thank you for addressing some points. I agree with you that the main objectives between both circuits are different - specially for a low quiescent & LDO regulator battery-powered. For non-battery operated circuits, richer in AC and HF switching noise, if -60dB is not enough with the regulator alone, I understand from you that it would be ok to add a CapMult as Ripple Smoother, with the ‘penalty’ of 1~2V for additional dropout. Ironically, this increased voltage drop would demand higher input capacitance to minimize voltage minimums and avoid loss of voltage regulation. \$\endgroup\$
    – EJE
    Jan 28, 2023 at 19:07
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To begin with, the capacitance multiplier is a block that, typically, is added on top of a voltage regulator to aid in ripple filtering.

As already pointed out by others, even by Dave Jones himself, the capacitance multiplier is simply meant to filter out high-frequency noise more effectively, while the voltage regulator's job is to keep the output voltage constant no matter the variations at \$V_{in}\$.

I'm not going to regurgitate what others have already pointed out, so I'm going to go with some of the other comments you made on a previous answer.

One of the reasons why ripple regulation could be disappointing in LDO in contrast to a capacitance multiplier is, that the typical LDO topology has roughly 3 dominant poles (error amplifier input, pass element and , which is a nightmare to compensate on in a feedback system. This will cause the LDO to be "crippled" in the sense that some aspects of it have to be given up in order to have stability and a usable range of bypass-capacitor/ESR combination that users can implement in their designs.

enter image description here Taken from Ricón-Mora's Current-Efficient, Low-Voltage, Low-Dropout regulators

In addition to that, a capacitance multiplier only filters out ripple without any regards to what DC input voltage it receives. Therefore, it is not a fair comparison to say that ripple rejection is worse in an LDO than in a capacitor "multiplier" without considering the rest of the LDO's job.

This brings me to the early reason for your question: is the capacitor multiplier an open-loop or a closed-loop type of system? I see your point of it being "open-loop" since it doesn't regulate voltage at all. However, since that's not its purpose, calling it an open-loop regulator seems a bit out-of-place.

I call it a closed-loop system because it's using an emitter follower, which uses series (input) - shunt (output) feedback.

How is, then, the emitter follower a closed-loop system? An emitter-follower can be modeled as negative feedback circuit because an increased in emitter voltage will lead to a decreased Vbe voltage, which in turn reduces the current through the transistor.

The voltage gain of a common-collector is given by (Assuming the load is $R_L$): $$ A_v = \frac{g_m R_L}{g_m R_L + 1} $$

You can consider the "open-loop" gain to be \$g_m R_L\$. However, as you can probably imagine, the \$g_m\$ is not constant along frequency, it will drop at higher frequencies.

By the same token, you'll find that the \$Z_{out}\$ of the emitter follower is scaled down by a \$(1+g_m R_L)\$ factor. It will go up with frequency.

You can do the math to prove to yourself that this is the case with the capacitance multiplier, too. This link: TF, Zin, Zout Capacitance multiplier derivation has more information about how to derive the expressions relevant to that circuit. You'll see that the output impedance are scaled down by beta (which equals \$g_mr_{\pi}\$).

IMHO, the most elegant way to remember this is to think of the nullor voltage follower implementation:

enter image description here

The emitter follower:

enter image description here

The op-amp voltage buffer:

enter image description here

(They're all, obviously, AC/small-signal schematic representations only, hence the grounding of the op-amp power supplies.)

In this way, it's easier to remember that, just as a the op-amp voltage buffer, the emitter follower also uses shunt feedback at the output. Shunt feedback will make your closed-loop output impedance very low (but not well-defined, to do so you need at least 2 loops at the output, but that's more complicated).

The output impedance will very low at DC, but it will grow as the loop gain drops at high frequencies => inductive-like behavior at the output. The voltage buffer will suffer from the same, only that its closed-loop output impedance will be much lower than the emitter follower due to huge loop gain available at DC.

From remembering this, you could've foreseen that, at least in theory, you could replace the emitter follower by an op-amp voltage buffer (of course, you have to add another resistor from input to output because the op-amp doesn't lend itself to sense current in series at its output; it only has one node, not 2).

And that is exactly the kind of circuit that Dave shows towards the end of the video. He argues, though, that it's probably not so good to use because of the current-handling and stability considerations of an op-amp, which are, usually, more restrictive than a single transistor. I agree with that.

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  • \$\begingroup\$ Thank you for your answer and clarifications, from where I would like to make some observations: (1) You can see the Title and paragraphs I wrote, I believe I meant Capacitance Multiplier is a Circuit, but not a Regulator - on the 3rd variant I said to be either seen (by a site) as a CapMult or a crude series regulator (from a buffered Zener) is when the R2 resistor (in yellow - 2nd variant) was replace by a Zener. All my questions were made around the ripple filtration, never about voltage regulation. And for this, I believe my views and all 3 answers are on the same page. \$\endgroup\$
    – EJE
    Jan 30, 2023 at 22:35
  • \$\begingroup\$ Maybe it was (my) choice of words, or a backlog of comments in the question, I don’t know, but: (2) Most answers were focusing about the fairness to compare the other features of a regulator. Dave’s experiments used a low power LDO, which I also see as “unfair” to the other features of it, as LDO regulation - but the focus/ main scope intended the would be the ripple rejection level per frequency. However, some answers seem sidetracked for this main point and potential reasons to explain that or oppose Dave’s findings. \$\endgroup\$
    – EJE
    Jan 30, 2023 at 23:06
  • \$\begingroup\$ (3) About the closed / open loop, that would be my interpretation to explain why a CapMult would be “faster” than a jelly bean voltage regulator - see examples I wrote. I appreciate you were the first to address the closed/open analogy, but I guess I was not lucky: A real voltage regulator has a closed loop with a feedback at circuit level, using several “complex” parts as transistor, OpAmp, RC networks, etc. Your explanation of feedback shows it at internal model of the transistor, but not at “circuit” level. In my “heretic” non-E.Eng. view, it would be an open loop at circuit level. \$\endgroup\$
    – EJE
    Jan 30, 2023 at 23:09
  • \$\begingroup\$ (4) I found the Rincon-Mora’s PhD thesis as a bit tough for me, saving it for later reading, as linked here; which you might consider updating your answer to review about the 3 poles (written just 2) and share the link too as I guess comments are considered temporary. picture.iczhiku.com/resource/eetop/shKrLKpyhGsZunxb.pdf. \$\endgroup\$
    – EJE
    Jan 30, 2023 at 23:10
  • \$\begingroup\$ (5) That link you posted seems very good to explain some points you said, but I still will need to study them. From its “Figure 7” could I understand that an internal feedback do exist as you said, internally to the transistor model, using “beta” and “g_M”. Still it would be much simpler that a “complex” regulator circuit (with all discussed other features). \$\endgroup\$
    – EJE
    Jan 30, 2023 at 23:31

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