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Power Supply 101 (Linear Supply)

DonH56

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This post (originally from ~2014) introduces the basic operation of a linear power supply, showing voltage and currents at the input and output.

There has been a lot of debate about power cords and their impact on the system. Aside from a defective or severely undersized cord I am a skeptic, largely because a few feet of cable is not going to change the rest of the wiring in your house and beyond. However, I do want to clear up some misconceptions about the bandwidth of signals coming out of your outlet. (OK, I admit that is a fanciful, wishful thought, but "clear up" is as good a choice of words as any for this). I am going to hand wave my way through a lot of technical details so purists please take note. This is not meant to be (and is not) a rigorous analysis.

I set up a very simple schematic (below). The voltage source represents the output of your power transformer. There are four diodes arranged in a full-wave bridge. For simplicity I used ten 1N4007A diodes in parallel to provide 10 A nominal current handling. The output drives (+) and (-) rail filter capacitors and load resistors. For this example the output voltage is going to be roughly 100 ~ 150 V so the resistors provide a constant load of 1 - 1.5 A. For this simple example I did not try to model an AC (dynamic) load that an amplifier in operation would present to the supply. Maybe later...

1687621063460.png


I ran a quick simulation to look at the input and output voltages and currents. The top plot shows the input voltage to the diode bridge in red and blue. The output after the diodes is shown in green and cyan (light blue). Now, diodes work only one way; that is, they conduct voltage (and current) in only one direction. You can see the output voltage rises with the input signal’s peaks and then drops between peaks. The amount of drop (droop) depends upon both the capacitors and the load current:

I = C * dV/dt

Where I = current, C = capacitance, dV = change in voltage, and dt = change in time. For a given load current, to reduce the droop (voltage ripple) we can increase the capacitance or decrease the time period between charging intervals. The former is a common mod; the latter is one reason switching supplies (that operate well above our 60 Hz line frequency – 50 Hz across the pond) are promising.

1687621092071.png


The bottom plot, showing the input and load currents, is very interesting. The output currents (red and green traces), into the load resistors, are pretty constant. Those great big current spikes (blue trace) are coming from the input voltage source, which ultimately represents the current drawn from your wall outlet. Those are the current spikes from charging the filter capacitors. They occur at the signal peaks when the diodes turn on and the supply has to charge up the capacitors, which have drooped during the diodes’ off time. Note they are much larger than the load current for this example. In the real world of audio amplifiers the load is not constant and things get a lot more complicated, but the point is that the input current in this simple static load case is mostly charging the capacitors in quick bursts. With load current of maybe 1.5 A, the input is supplying ~8 A peaks to charge the filter capacitors.

Looking at the top spectral (FFT) plot, the input voltage is essentially a single peak at 60 Hz as expected. Also expected, the output is mostly DC (0 Hz) with a 120 Hz ripple current from the full-wave diode bridge. The load current spectrum (bottom plot, green trace) is essentially the same as the load voltage, but you can see a series of spurs extending past 600 Hz for the input current. Not very high frequency, but remember this is from the wall socket, thus it is ten times the fundamental wall frequency.

1687621127851.png


The obvious question is how this changes if we increase the filter caps to reduce the output ripple. The results (below) may be surprising… You can see the ripple voltage is greatly reduced going from 100 uF to 1000 uF capacitors, but the current spikes are much larger! The output current has been smoothed much as the output voltage, but the input current spikes are much larger. Remember current (I) is directly related to capacitance (C) so the larger capacitors are demanding much more current during the charging cycles even if the load is not. Since my input voltage source is ideal, it provides the current demanded, and you see the results.

1687621143637.png


The FFT’s show reduced ripple voltage and current at the output but reflects the larger current spikes with energy past 1 kHz.

1687621158818.png


What does all this mean for a power cord? Well, if we had a superconducting power cord it would still be limited by the wall socket. Having a cord the same gauge as the wire in the wall to the socket is quite probably good enough. A cord that adds a shield and capacitance might help reduce the frequency content of the current spikes that gets both radiated and drawn from the wall. I have no idea if the aftermarket cords help with that. Finally, any connection can add resistance, so clean, tight plugs and jacks could certainly be important. It is quite possible (at least in my mind) that some of the benefit of a cable swap is due to simple wiping action that cleans oxidation off the connections and provides lower power impedance. Swapping back to the original cable, or better yet having somebody do it for you at a time unknown to you, might help determine if that is the case.

Finally, this is meant to be a quick look and is by no means representative of all the possible cases of supply and load interaction. It does not include a dynamic load, and provides no insight about an amplifier’s resistance to power supply ripple (PSRR) or anything else. I merely wanted to show folk who might not have ever looked at the signals around their power supply some of the things going on.

FWIWFM, HTH, etc. – Don

Edit: One thing not considered is the transformer itself. I did not have a good model back then (2014) and figured this was good enough an example. The transformer will act as a filter to smooth the pulses and reduce the HF content, further reducing demands upon the power cord (wall supply, etc.) This analysis is also not applicable to SMPS circuits since they operate very differently, though the power cord should still have negligible influence on the power supply output (less, actually, since SMPS’ include regulation by design). And of course SMPS (switch-mode power supplies) have fundamental frequency well above the audio band, so unlike linear supplies there are no 50/60 or 100/120 Hz fundamentals and harmonics to corrupt the audio band (leakage excepted). Finally, some power cords may (may!) include RFI filters, though any decent component design will include that internally and not depend upon the power cord (that could be replaced later).
 

DVDdoug

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There has been a lot of debate about power cords
It's a "debate" between audiophools (or ignorant people) and rational people.

For simplicity I used ten 1N4007A diodes in parallel to provide 10 A nominal current handling.
Not a good "permanent" design. You can't guarantee that the current will divide equally. And if one diode fails & shorts out all kinds of bad things happen.

You can see the ripple voltage is greatly reduced going from 100 uF to 1000 uF capacitors
You won't find 100uF filter caps in a power amplifier.

In a "good design" there will be a voltage regulator and besides regulating the voltage it will filter out (most of) the remaining ripple (and it will also help with any other noise that gets-through the transformer).
 

blueone

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Great post, Don, as usual. One topic that would be great to add is a discussion of the controversy about how adding smoothing capacitance can increase peak current output. One article I've read called this "complete rubbish", yet I still read that additional capacitance can increase current output in posts and articles from people who would seem should know better if it is rubbish. Can you discuss this factor further?
 

fpitas

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SIMing the effect of RC snubbers on the diode reverse recovery might be interesting, too.
 
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DonH56

DonH56

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It's a "debate" between audiophools (or ignorant people) and rational people.

Not a good "permanent" design. You can't guarantee that the current will divide equally. And if one diode fails & shorts out all kinds of bad things happen.

You won't find 100uF filter caps in a power amplifier.

This was not in any way or form a real design, just a simulated example to show people without engineering backgrounds some of the key waveforms and such.

In a "good design" there will be a voltage regulator and besides regulating the voltage it will filter out (most of) the remaining ripple (and it will also help with any other noise that gets-through the transformer).

Most power amplifiers do not have regulated (linear) supplies for the output stages. The original post was in response to that application, sorry I did not copy that background over.
 
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DonH56

DonH56

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Great post, Don, as usual.
Thank you!

One topic that would be great to add is a discussion of the controversy about how adding smoothing capacitance can increase peak current output. One article I've read called this "complete rubbish", yet I still read that additional capacitance can increase current output in posts and articles from people who would seem should know better if it is rubbish. Can you discuss this factor further?
Um, yes, but not sure I want to head down that rabbit hole in this introductory thread. Handwavingly, consider that a full-wave rectifier as shown here "tops off" the capacitors at 120 Hz, so faster signals are going to be pulling from the capacitors between "recharging" cycles. So during that time more capacitance, assuming it can provide the charge quickly enough (not usually an issue), can provide greater current before the voltage sags. The basic equation is i = C* dV/dt which re-arranged is dV = i/C * dt. In these equations, "d" represents change, so bigger capacitors (C) means you can provide greater current (i) without increasing the voltage ripple (dV) given the same time period (dt). There are a myriad of details and "what if" trades in practice, natch, that determine how much and if extra capacitance provides meaningful improvement.
 

fpitas

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I guess subjects like reverse recovery are a little beyond your scope.
 
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DonH56

DonH56

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SIMing the effect of RC snubbers on the diode reverse recovery might be interesting, too.
I guess subjects like reverse recovery are a little beyond your scope.

Well, maybe not "my scope" ;) , but probably beyond this thread's scope for the target audience. I actually have a presentation on that, but I gave it at work so they own the slides (even though it is basic stuff). My presentation was geared towards SMPS designs and not a simple linear supply (though principles are the same), and mainly to help explain how noise gain and resonances can really mess things up without snubbers. For now I need to prep for a concert tonight so I'll table that for later (hopefully I'll remember but no promises!) There are pros and cons, natch, like everything else. Not just for snubbers, but whether faster recovery diodes help or hurt (can go either way). I am not a power guy so perhaps that's something you'd care to present? I'm lazy...
 

pma

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"Standard" linear power supply, with EI transformer, +/- 15V output, LM7815/LM7915 stabilizers in a conventional scheme, has quite excellent S/N parameters and spectrum

Linear_PSU_uA7815_68mA_1.png

Red line corresponds to +15V output voltage. 100Hz line is 106dB below. Mains residuals are quickly attenuated. S/N (45kHz) is 101.36dB.


With wider BW
Linear_PSU_uA7815_68mA_2.png

Spectrum is clean above 1kHz up to 80kHz.
 

Sokel

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"Standard" linear power supply, with EI transformer, +/- 15V output, LM7815/LM7915 stabilizers in a conventional scheme, has quite excellent S/N parameters and spectrum

View attachment 294792
Red line corresponds to +15V output voltage. 100Hz line is 106dB below. Mains residuals are quickly attenuated. S/N (45kHz) is 101.36dB.


With wider BW
View attachment 294791
Spectrum is clean above 1kHz up to 80kHz.
It would be valuable to have an exact (most around the net is almost generic) schematic for a nice 15-0-15 to follow.
I mean the exact value components,layout,etc.
 

solderdude

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But what is nice ?
What power rating ?
stabilized ?
Mains filtering ?
Transformer type ?
Low noise ?

In most cases the actual application it is to be used with determines the design.
 

Mnyb

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Thanks nice writeup .

The obvious follow up question what about LC or LCL or LCLC type of linear supplies :D

I reckon they are(where) common in Tube gear of old ( And the LC type is in industrial VSD drives with sometimes some LCL filter at the input too )

Nowadays when building power amps a normal linear supply as you described is deemed "good enough" even in expensive amps and any upgrade is usually a switchmode supply like in the AHB2 ?

Not seen anyone going to the extra trouble off adding heavy and large filter inductors in linear power supplies in a long time.
The cynic in me tells that its not an understood and marketable feature , moare microfarads is :)
 

fpitas

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Thanks nice writeup .

The obvious follow up question what about LC or LCL or LCLC type of linear supplies :D

I reckon they are(where) common in Tube gear of old ( And the LC type is in industrial VSD drives with sometimes some LCL filter at the input too )

Nowadays when building power amps a normal linear supply as you described is deemed "good enough" even in expensive amps and any upgrade is usually a switchmode supply like in the AHB2 ?

Not seen anyone going to the extra trouble off adding heavy and large filter inductors in linear power supplies in a long time.
The cynic in me tells that its not an understood and marketable feature , moare microfarads is :)
A useful series inductor has obvious drawbacks, such as size, cost and weight. Back when speakers had a field coil that served well, more or less for free.
 

Sokel

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But what is nice ?
What power rating ?
stabilized ?
Mains filtering ?
Transformer type ?
Low noise ?

In most cases the actual application it is to be used with determines the design.
1A must be sufficient for stuff like pre's,active X-overs.etc.
Yes.
Yes.
The most common around,about 30VA,double windings.
Yes.

(the simpler,the better)
 

Mnyb

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A useful series inductor has obvious drawbacks, such as size, cost and weight. Back when speakers had a field coil that served well, more or less for free.
yes they are , but they are not even there in veblen ultra expensive hifi where cost size and weight and price are desired features :)
Just curios why all seems universally happy with the more common solutions we have .
In economically/sanely designed gear where you weigh pros and cons i do completely understand why they are omitted as the cost of the inductors easily gives a lot of voltage regulators for example :) or other things that gives your design better performance .
 

fpitas

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1A must be sufficient for stuff like pre's,active X-overs.etc.
Yes.
Yes.
The most common around,about 30VA,double windings.
Yes.

(the simpler,the better)
Pre-made linear supplies are commonly available, unless you just want to build your own.
 

fpitas

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yes they are , but they are not even there in veblen ultra expensive hifi where cost size and weight and price are desired features :)
Just curios why all seems universally happy with the more common solutions we have .
In economically/sanely designed gear where you weigh pros and cons i do completely understand why they are omitted as the cost of the inductors easily gives a lot of voltage regulators for example :) or other things that gives your design better performance .
Some tube guys still use them. More for nostalgia than engineering, I would say.
 
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