How to Judge the Linearity of a Dependent Current/Voltage Source

[FAS1998]

TL;DR

How do we know when a dependent source is linear?

How can we evaluate the linearity of a dependent voltage/current source? Components like resistors are easy to deal with because they always obey a linear equation. Dependent sources are more complicated because their voltage/current relationships depends on other parameters within the circuit.

 

[Tom.G]

1) Take input and output measurements for at least 3 operating points that cover the range of interest.
2) When the points are plotted on ordinary linear graph paper (quadrile paper for example), they will be on a straight line if linear.
2a) You can also divide the output by the input at each point and the answers will match if linear.

The above is the first approximation, and often sufficient. More detail can be obtained by measuring at more than 3 points across the range.

If it is an AC circuit, you may want to do the above at various frequencies within the bandwidth of interest.

Cheers,
Tom

 

[FAS1998]

1) Take input and output measurements for at least 3 operating points that cover the range of interest.
2) When the points are plotted on ordinary linear graph paper (quadrile paper for example), they will be on a straight line if linear.
2a) You can also divide the output by the input at each point and the answers will match if linear.

The above is the first approximation, and often sufficient. More detail can be obtained by measuring at more than 3 points across the range.

If it is an AC circuit, you may want to do the above at various frequencies within the bandwidth of interest.

Cheers,
Tom

How would you determine the linearity of a theoretical dependent source from its corresponding equation? You wouldn't be able to take input/output measurements in this case.

 

[Tom.G]

If you can't determine if the equation is linear, plug in some values for input and calculate the output; then follow post#2 above.

After that, refresh you mathematics knowledge enough to recognize linear vs non-linear equations.

Cheers,
Tom

 

[FAS1998]

If you can't determine if the equation is linear, plug in some values for input and calculate the output; then follow post#2 above.

After that, refresh you mathematics knowledge enough to recognize linear vs non-linear equations.

Cheers,
Tom

But dependent sources usually have equations like V = 5v1, where v1 is the voltage at some node present in the circuit. This equations shows a clear linear relationship between V and v1, but that isn't what determines the linearity of the component if I'm not mistaken. We need to know about the relationship between V and I, the voltage and current across the component. I'm not sure what values can be tested in this context.

 

[Tom.G]

V = 5v1, ...
This equations shows a clear linear relationship between V and v1, but that isn't what determines the linearity of the component if I'm not mistaken.

If the equation is completely describing the component, then it does indeed show that component to be linear; that is, its output is invariably five times its input.

In a simulation, the description given, V=5v1, is used to compute the output from a given input.

You may be thinking 'What happens if the input is non-linear.' The input doesn't change what that component is doing. That component is only multiplying its input by 5.

All components in the real world do have their limitations though. For instance if you have a flashlight bulb rated at 3 Volts and connect it to a wall outlet, it's not very useful (it may be spectacular though). (Please don't try it without lots of safety precautions!)

Cheers,
Tom

 

[Baluncore]

How can we evaluate the linearity of a dependent voltage/current source?

If you look closely enough at big enough signals, everything real will have some non-linearity. Insulators won't insulate or conductors will fuse.

You must define how much non-linearity you can tolerate under what conditions.
Are you concerned with the linearity of the controlling signal versus the controlled output voltage / current? Or with the linearity of the output voltage / current versus the load current / voltage?

The quickest test for non-linearity would be to inject a two-tone sinewave signal. If the circuit is non-linear you will see new frequencies appear in the output at sum, difference and multiples of the input signal frequency components.

All components in the real world do have their limitations though. For instance if you have a flashlight bulb rated at 3 Volts and connect it to a wall outlet, it's not very useful (it may be spectacular though). (Please don't try it without lots of safety precautions!)

I did that brightness "experiment" when I was about 7. The light globe was non-linear, and became discontinuous in the time domain. I never found any glass from the flashlight bulb. After the bigger than expected surprise, I switched off the power, and replaced the 240V bulb in the socket. I told my mother that my light did not work. The fuse for that circuit was replaced later.
You can learn a lot from experimentation, if you survive.

 

[sophiecentaur]

This thread is going the same way as 'the other' parallel one. Linearity is never perfect and it doesn't necessarily get worse with large signals. The well known Crossover Distortion in many (push pull) audio amplifiers introduces irregularity of the transfer function as the signal goes past Zero. Worse for low levels.
If you want to measure linearity then the most sensitive way is to base it on Intermodulation Products. Put two good sinusoids through an amplifier / codec / passive transducer and look for intermodulation products at sum and difference frequencies (and higher orders). Total Harmonic Distortion is a poor man's version measurement but it doesn't work for narrow band RF amplifiers (and you find those everywhere) where harmonics cannot be measured meaningfully.
You have to specify what's good enough and test to that spec. Even a piece of wire can have non linearity at its terminals.