# Could PWM be applied to emulate resistance?

1. Mar 3, 2017

### rumborak

This thought occurred to me when reading about class D amplifiers, which essentially "emulates" amplification by very quickly switching on and off.
Could one use the same principle to eliminate for example heat losses during impedance matching? IIRC, in the perfect condition of matched impedance, 50% of the energy is lost. Would it possible to eliminate the input impedance by "emulating" it through rapid switching the current?

2. Mar 3, 2017

### Averagesupernova

First you need to understand the reason for impedance matching. In many cases it simply does not matter. We drive subwoofers with class D to eliminate ANY output impedance from wasting power as heat. This is most certainly a case where impedances are not matched and it does not matter. Where it mostly matters is when we are using transmission lines that are a significant portion of a wavelength of the signals involved.

3. Mar 3, 2017

### rumborak

The impedance matching I mostly mentioned because it seemed a natural candidate. Overall I'm actually more interested in the general idea of approximating resistance through high-frequency current switching. There might not be any useful application, it just struck me as an entertaining thing to think about.

I guess you couldn't use it to lower transmission loss either really. Say you wanted to approximate 1A by quickly switching between 0A and 2A. Because of P=R*I^2, you'd actually lose 4 * 0.5 = 2 times the amount of heat loss on a wire.

4. Mar 4, 2017

### Baluncore

The 50% you refer to is probably the special condition where the series resistance of a source or generator equals the load resistance. That represents the maximum possible energy flow to the load from the generator. But you do not want half the entire available energy of the power grid to appear in your house.
I think you are confusing impedance with it's two components, resistance and reactance.

5. Mar 4, 2017

### rumborak

Well, it's the resistance, I.e. the real aspect of the complex impedance, is the one that creates the heat loss.
But yeah, as I said, this was little more than a thought experiment :) I figured I'd ask whether this "fast switching" concept had been applied elsewhere in electronics.

6. Mar 4, 2017

### Baluncore

Yes it can be applied, but the PWM frequency needs to be well above the bandwidth of the external circuit.

Consider an LC low pass filter. Use PWM to keep the current flowing through the inductance, L, proportional to the external voltage across the circuit. By PWM switching at a frequency above the LPF cut off frequency you can make the LC filter input look like a resistor at low frequencies.

When you emulate a resistor with a switching circuit, where does the very real power go ?
What implications does that have for power supply design specifications ?

7. Mar 5, 2017

### rumborak

I think to some degree my motivation to ask this also comes from the fact that it always bugged me a bit that in circuits, resistors always felt like a rather clunky way to achieve a certain goal. For example, take a pull-up resistor, whose main role is to merely adjust the potential at a certain point in the circuit.
But, now you got constant power loss from this resistor, just to achieve that shift. I wonder how much power could be saved if this stuff could be achieved in a different way.

8. Mar 5, 2017

### Baluncore

Resistor current is not really the problem you seem to fear. Where a pull-up resistor is used, current only flows when the signal is low. A good design will not keep that signal low any longer than is needed. 200uA at 5V is only 1mW.

9. Mar 5, 2017

### rumborak

I mean in general though, many circuit parameters are achieved by a "controlled burnoff" of energy in that sense. You may have a voltage divider etc, all these things just throw away energy in order to achieve a reasonably unrelated effect, e.g. adjusting the voltage, or constraining the current. Ideally, there would be a different way to achieve this. It's a bit like throwing a space heater in series with your light bulb just to dim the bulb a bit.

10. Mar 5, 2017

### Averagesupernova

So what's this all about? Replacing all single transistors and a pullup with push pull stages?

11. Mar 5, 2017

### rumborak

I feel I'm not doing a good job here at explaining. From my side this is a very abstract discussion of "are there are other, less lossy ways to achieve circuit parameters, without just blatantly burning energy to achieve it". Initially I suggested the PWM to achieve this.

12. Mar 5, 2017

### Averagesupernova

I suspect that you assume there are places where we needlessly burn up thousands of Watts just for impedance matching but this is generally not the case. If we take a class B amplifier that would drive a loudspeaker by definition we burn up a portion of energy to achieve a voltage somewhere between the supply rails. This is because the output transistors and the loudspeaker form a voltage divider to get the desired voltage at the loudspeaker. It isn't because we are trying to satisfy matching impedances. Class D found a way around that as you have pointed out. A switching power supply does the same thing compared to a linear supply with a pass transistor.
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People get all wrapped up in impedance matching.
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What the theorem states is this:
If we have a 10 volt source with an output impedance of 100 ohms for instance and we try to drive a load with 100 ohms. Half the voltage will be dropped in the load and half in the source. We dissipate a quarter watt in the source as well as a quarter watt in the load. This is the most power you will transfer from the source to the load. If you increase the load to say 150 the load now only receives .24 watts. If we decrease the load to 50 ohms the load now receives .222 watts.

13. Mar 5, 2017

### rumborak

I would say burning 50% of your total energy expenditure on useless heat is pretty bad.

But I feel a bit bewildered that you came back to the impedance matching part. As I pointed out, that's just an example; my point here is that using resistors, of any kind, is a pretty clunky way to achieve circuit design goals. I'm not sure there is a solution, but I was hoping for a more high-level discussion about the topic.

Hmm, I might repost this thread in a modified form in GD under a more physics-oriented angle. That is, can you achieve voltage/current goals usually achieved by resistors by other means.

Last edited: Mar 5, 2017
14. Mar 5, 2017

### Averagesupernova

And I asked you if you thought we should eliminate all pullup resistors and replace them with push-pull transistor stages and didn't get a reply other than that resistors are clunky. Consider how far we have come. Switching supplies, LED lighting with switching drivers, class D and C amplifiers. Not to mention the fact that we had light dimmers for incandescent that were basically switching (phase angle) before incandescent bulbs were phased out in favor of something more efficient. They used to use actual rheostats where the excess was wasted as heat. The power lost in eighth and quarter watt resistors isn't really relevant considering other losses we accept.

15. Mar 6, 2017

### Rive

Yes//no.
The very function of a resistor is to lose energy => any kind of emulation of a resistor would require to lose energy. You just cannot spare that.
In theory, it's possible to recover some of that energy, but most of the times it's just not practical.

However, the 'yes' part. There are situations when you have to know how much energy is removed and when exactly. So for example the PFC circuit in the PSU of your PC is doing a kind of switch mode impedance matching.

Also, for battery testing the traditional solution is to provide stable discharge current (or: voltage)with a linear amplifier. Alternative is, to use a special switch mode circuit to recover the energy and feed it back to a power rail, while keeping the constant current for the battery.

Last edited: Mar 6, 2017
16. Mar 6, 2017

### Baluncore

A switching circuit can only efficiently emulate a resistor at lower frequencies. That is because there must be a low-pass filter to keep the switching bandwidth out of the signal bandwidth. Any switching circuit will waste more power than the signal resistor or pull-up resistor it emulates.

rumborak: You have not answered those two key questions. They are critical to understanding the emulation of resistors.

17. Mar 6, 2017

### rumborak

The point of the exercise wouldn't be to emulate a resistor entirely, because as you say, then you would of course have to emulate the heat loss.

Think of a really simple example, e.g. two resistors of equal value, all in series with a battery. That constitutes a voltage divider, and many times it's used in a circuit to achieve a certain voltage against ground, because now you have half the voltage over each resistor.
However, the *actual* goal here was to get a different voltage than the battery voltage, but by using resistors you burn a ton of energy, solely to achieve that voltage goal.
So, the question is, could you for example use only one resistor, but switch the current at a very high frequency so *on average* that resistor "sees" only half the current, and thus *on average* also only half the voltage.

I think the above also covers @Baluncore 's question towards me. I'm not trying to magically make energy appear; rather, I'm wondering whether the, IMHO somewhat clunky, use of resistors to achieve secondary goals such as constraining the current or having voltage drop, could be instead achieved in different ways that don't waste energy in the process.

18. Mar 6, 2017

### Rive

That's actually a (very common) DC-DC converter, right?

19. Mar 6, 2017

### rumborak

Good point. The Wiki article on it also mentions that the challenge is parasitic effects that make it hard to use them in circuit design. So, arguably one *could* use them for the purpose I mention (and the article also mentions reduced heat sink requirements), it's just not feasible.

If I understand correctly, the DC to DC converter is a true black box that you can throw in as a replacement for any voltage need, I.e. the high frequency switching is entirely contained in it, with the outside none the wiser. I wonder whether an entire circuit could be made to work with the OEM switching, thus alleviating the constraints of DC/DC converters.

Nonetheless, I feel it's interesting to note that dropping voltage does *not* require energy loss per se. Can you constrain current without heat loss?

20. Mar 6, 2017

### Baluncore

NO you would NOT have to waste heat. You can use the energy somewhere else.
My two questions need sensible answers if you are to understand what is happening.

Increase the resistor values, add a capacitor, use a FET follower to reduce the load.

That would also waste energy. Instead, find somewhere with a square wave in the circuit. Use an LC filter to average that square wave. The currrent in the L is reactive. You then have your Vcap = Vref = Vbatt / 2 without any significant R losses.