Application of the superposition theorem

[Richardcavell]

Hi, everyone. I have learned how to use the superposition theorem to calculate the voltage/current of each component in a circuit with multiple sources.

1. Can the theorem work for a circuit that has current sources and voltage sources mixed together?

2. What is the practical application of a circuit that has multiple such sources? I realise that it would be useful, say, to have one circuit that creates a signal and feeds that to a second circuit that acts as an amplifier, for example. But what about where there are two voltage sources of comparable voltage?

3. I have always viewed voltage sources as a battery of 1.5 Volt cells. These cells supply 1.5V (approx.) at whatever current is drawn, until they're dead. I find it difficult to conceptualise current sources, though. Is there a real-world current source that I can use to conceptualise such things?

4. A battery of 1.5V cells, in my experience, is used to provide currents at about 1 to 100 milliamps. What kind of voltages should one expect from a current source?

Richard

 

[Ratchit]

Richardcavell,

The following answers are based on the premise that all the sources are at the same single frequency. Superposition can be used for multifrequency sources too, but calculations have to be based on RMS values which I will not touch upon.

1. Can the theorem work for a circuit that has current sources and voltage sources mixed together?

Yes, as long as the circuit components are linear. Both AC and DC analysis can be done.

2. What is the practical application of a circuit that has multiple such sources? I realise that it would be useful, say, to have one circuit that creates a signal and feeds that to a second circuit that acts as an amplifier, for example. But what about where there are two voltage sources of comparable voltage?

The value of the voltage makes no difference. As long as the circuit is linear, the result is the sum of each contribution.

3. I have always viewed voltage sources as a battery of 1.5 Volt cells. These cells supply 1.5V (approx.) at whatever current is drawn, until they're dead. I find it difficult to conceptualise current sources, though. Is there a real-world current source that I can use to conceptualise such things?

A battery should always be viewed as a voltage in series with a internal resistance. The more current that exists, the more the internal resistance decreases the output voltage. A more perfect voltage source is an electronically regulated voltage source, where the output voltage is sensed, and kept at a determined value.

Again, a electronically regulated current source is the best choice. Otherwise, a large voltage in series with an appropriate large resistor will approximate a current source. For instance, a 1000 volt source in series with a 1 meg resistor will make a fairly good 1 ma current source. There will be 1000 volts of authority that says 1 ma will pass through a circuit. Most applications don't require that much voltage, however.

4. A battery of 1.5V cells, in my experience, is used to provide currents at about 1 to 100 milliamps. What kind of voltages should one expect from a current source?

Ideally, a current source should apply whatever voltage is necessary to make the designated current exist. In the real world, the forcing voltage is finite. Perfect current sources have infinite internal resistance, and perfect voltage sources have zero internal resistance.

Ratch

 

[Diver300]

2. What is the practical application of a circuit that has multiple such sources?

A car alternator is a constant current source, if you look at it short-term. The voltage regulator will take a second or so to respond, so on very short time scales the current is just about fixed.

When you turn on the car headlights, the filaments are cold and have much less resistance. They take maybe 30 amps each side for a very short time, so that 60 A has to come from somewhere. The alternator can't provide it as it can't respond that quickly, so the battery takes up the slack. The battery can be looked at as a voltage source with a low resistance.

The situation changes as the filaments warm up and as the alternator's voltage regulator responds.

As for multiple sources, it is quite common to have aerial cables with DC flowing one way to power amplifiers and AC signals going the other way. This is done for satellite receiver LNBs and for GPS active antennas.

 

[Diver300]

3. I have always viewed voltage sources as a battery of 1.5 Volt cells. These cells supply 1.5V (approx.) at whatever current is drawn, until they're dead. I find it difficult to conceptualise current sources, though. Is there a real-world current source that I can use to conceptualise such things?

In transformerless power supplies, there is a capacitor that limits the current taken from the mains. The low voltage part of the circuit has to take the current or go bang. Although the voltage is only 120 or 230, not infinite, if you are lighting LEDs the voltage is far larger than any of those components can stand, so the circuit has to handle the current somehow.

For a hydraulic analogy, a battery is like a water tank or a lake. You can take flow from it if you want, but you can leave it where it is.

A current source is like a river coming from high in the mountains. There is a certain flow arriving and you had better be able to deal with it. If you don't want to do anything with it, let if flow to the sea. That is like earthing the output of a current source.

 

[crutschow]

A car alternator is a constant current source, if you look at it short-term. The voltage regulator will take a second or so to respond, so on very short time scales the current is just about fixed.

A car alternator (as true for most types of generators) has a low output impedance so it really is not much of a current source. It's true the alternator voltage will drop slightly with a sudden increased load until the regulator can respond, but that doesn't make it a current source. Even if the regulator did not readjust the voltage, the alternator would still deliver more current when the load increased, as determined by the internal winding impedance of the alternator.

 

[Diver300]

A car alternator (as true for most types of generators) has a low output impedance so it really is not much of a current source. It's true the alternator voltage will drop slightly with a sudden increased load until the regulator can respond, but that doesn't make it a current source. Even if the regulator did not readjust the voltage, the alternator would still deliver more current when the load increased, as determined by the internal winding impedance of the alternator.

"Load Dump" is when an alternator suddenly becomes unloaded. Voltages up to 80 V for 1/2 second can be generated. If you look at the typical test specifications in https://www.emtest.com/products/product/102180100000010235.pdf you'll see that the voltages are often above 80 V.

I don't regard that as a slight rise in voltage. Similarly, without a battery, a big increase in load will reduce the voltage by a lot, until the regulator can increase the output.

The fact is that car alternators are just about never run without a battery. That is why their short-term constant current characteristics are never noticed, but that doesn't mean that a car alternator on its own would run a car satisfactorily.

A friend of mine had a battery fail completely while he was driving. When he turned his headlights off and on, the car lost all power for a couple of seconds. The alternator just couldn't provide any enough current to light the headlights.

 

[MrAl]

Hi, everyone. I have learned how to use the superposition theorem to calculate the voltage/current of each component in a circuit with multiple sources.

1. Can the theorem work for a circuit that has current sources and voltage sources mixed together?

2. What is the practical application of a circuit that has multiple such sources? I realise that it would be useful, say, to have one circuit that creates a signal and feeds that to a second circuit that acts as an amplifier, for example. But what about where there are two voltage sources of comparable voltage?

3. I have always viewed voltage sources as a battery of 1.5 Volt cells. These cells supply 1.5V (approx.) at whatever current is drawn, until they're dead. I find it difficult to conceptualise current sources, though. Is there a real-world current source that I can use to conceptualise such things?

4. A battery of 1.5V cells, in my experience, is used to provide currents at about 1 to 100 milliamps. What kind of voltages should one expect from a current source?

Richard

Hi Richard,


When you have multiple sources of any kind (constant voltage or constant current) you "kill" all the sources and then "unkill" them one at a time and compute each response. After all responses are calculated you then add up all the responses and that is the actual total response. The only catch is that to kill a voltage source you short circuit it, but to kill a current source you open circuit it. To unkill a voltage source of course you connect it back up normally, and to unkill a current source you simply connect it back up normally too.
You only unkill one at a time as noted, and once you have the response for that source, you then kill it again before proceeding to unkill the next source. Thus the process goes like this:

1. Kill all sources.
2. Unkill one source only and calculate the response for that source, then kill it again.
3. Repeat #2 above until all sources have been done with all individual responses calculated.
4. Add up all the individual responses calculated in #2 above to get the total response.

Just one more little thing...

If you try this with a real circuit when you kill a voltage source you have to first disconnect it and then short out the two nodes it had connected to, and when you kill a current source you have to first short it out and then disconnect one of the nodes completely to disconnect it from the circuit. Of course you may also have to turn off the voltage or current first which makes sense.
With the theoretical circuit we dont have to worry about doing these things.