# Simple examples of higher order circuits and the cause of non linearity

In my previous question, I learned that resistance, capacitance, and inductance are not enough to capture the behavior of all circuits. This led me to the question, what are some examples of 'simple' nonlinear circuits in our daily life?

And, what exactly is it which causes the circuits to behave in a nonlinear way?

Difference between this and the previous post: I have asked about why we need three quantities to describe most phenomena in linear circuits, here I for examples.

This led me to the question, what are some examples of 'simple' nonlinear circuits in our daily life?

Anything with a diode, or a transistor is a non-linear device. The output does not always scale to the input (some transistors can be put in a linear mode, but saturation prevents them from being fully linear).

And, what are the new parameters introduced to study them

If you want to analyze them, then you need to use linear tools, and model them with laplace. (even spice simulators linearize non-linear components to analyze the system as a whole). If you are constructing a design around a DC operating point, small signal models can be used to calculate linear models.

Non-linearity effects change in a constant or linear function include;

• harmonic distortion, clipping non-linear VCO’s, saturation, dead-time , reverse recovery time, spurious oscillations, negative incremental impedance in a net positive resistance, etc. saturation of inductors , decline of capacitance in ceramic caps vs Vc, thermal, mechanical , vacuum, humidity and aging effects,

Higher order effects include;

• parasitic LC mutual coupling with L changing with dc current

• harmonic effects of multiplying a frequency with non-linearity causing intermodulation, 3rd order intercepts 3OI etc.

Daily life example ?

• the gas pedal on your car might not give linear acceleration with force.

• Your coffee maker has a thermal switch with hysteresis to regulate heat around a preset average temperature.

For a simple transistor , any changes in Vbe cause non-linearity.

• Consider the common emitter config. with an emitter resistor in series with re which reduces with rising Ic. This makes it more linear as the base voltage now controls emitter voltage (keeping Vbe more constant) and thus controls Ie and Ic .
• Negative feedback also reduces the variation in Vbe if there is a source impedance to make a voltage ratio and thus also reduce gain. Now Re can be made quite small equal to re or 0 ohms to maximize the open loop gain and thus achieve at least half of the Rfb/Rin gain ratio. The excess gain now reduces the 2nd order harmonic distortion cause by variations in Vbe.

The simplest non-linear component in our daily lives is.... the resistor. They are only linear when you learn about them in school.

In reality their resistance depends on the voltage applied, temperature, humidity, age and more. They also have inductance and capacitance. To be fair though they behave close enough to their ideal form.

Welcome to the real world!

• Dependency on temperature, humidity and age doesn't make a resistor a non-linear device. Neither is non-linearity introduced by additional capacities and / or inductances. A resistor would be non-linear only when its resistance depends on the applied voltage. As no real component has ideal properties one never could say that an resistor is a perfectly linear device. But a resistor is really not a good example when explaining non-linearity to a beginner. – Elec1 Jun 17 at 17:13
• If you consider self-heating, temperature dependence kind of makes it non-linear. But I think we are just splitting hairs here. I agree with you. A resistor is as linear a component as onr can find. – Grease Monkey Jun 17 at 17:46