# Linear Devices in Electronics and How They Affect Your Signals

## Table of Contents

Many cultures view time as linear or as something that moves along a straight line. The flow of time moves from past to present to future.

Other cultures, however, have a different perspective about time. Those see time moving in cycles. History repeats itself and all human events occur in cycles.

Linear devices in electronics have nothing to do with how we perceive time, but they do matter for how your circuits perform and how they should be designed to accommodate different signals. The other type of electrical behavior you'll find in components and integrated circuits is a nonlinear electrical response. Understanding these points is very important for circuit design, especially as more PCB designers now also need to put on their electrical engineering hats and design circuits. Here's how these different types of circuits and components behave electrically, and what it means for your PCB design.

## Basics of Linear Devices in Electronics

### Linear vs. Nonlinear Circuits

In electronics, we can separate devices according to linear and non-linear operation. Linear devices in electronics have their output signal as a linear function of the input signal. In other words, the two are directly proportional. We can go all the way back to Ohm’s Law to find that any increase in applied voltage leads to an increase in current if the resistance remains the same. As a result, all the basic circuit parameters—such as resistance, inductance, capacitance, waveform, and frequency—do not change with respect to current and voltage. Current flowing through a linear circuit is directly proportional to the applied voltage.

In contrast, nonlinear circuits do not have their output and input related by a straight line. For example, consider a typical pn diode. The current in the diode is an exponential function of the voltage dropped across the diode. As a result, all other important signal qualities we might want to measure for an arbitrary signal are a function of the input signal level. This includes the time-domain waveform which may not resemble the input waveform at all due to strong nonlinearity.

An example is show below for an AC voltage applied across a pn diode with ideality factor = 1.5. The diode in this example calculation is driven with a 1 Hz sine wave. When the amplitude of the sine wave is low (1 mV), the current waveform in the diode is basically exactly the same as the input sine waveform. There are extremely minor deviations, but these deviations are so small that you'll probably never measure them. As the input voltage amplitude is increased to 100 mV and 1 V, we see how the sine waveform produces a rectified pulse-type waveform.

This distortion of an input waveform at high input signal level is fundamental electrical behavior of nonlinear circuits and components. Therefore, it's important to know when nonlinear effects start to become apparent when designing circuits and how to deal with them if they do happen.

### Which Components are Nonlinear?

There is a dirty little secret that most engineers don't realize and most physicists won't tell you: every electronic device that has ever been made or ever will be made is nonlinear! However, there are components where you will never measure the nonlinear behavior of the component at practical signal levels and conditions. The device will either break when the input level becomes too high, or the nonlinear behavior is too weak to be noticed in practical situations.

That being said, we can classify some common components as linear or nonlinear:

- Linear devices include resistors, capacitors, and most inductors when driven with low current.
- Nonlinear devices include semiconductor devices (transistors and diodes), ferrite inductors driven at high current where magnetic saturation occurs, all amplifiers, and almost all integrated circuits.

Transistors and integrated circuits are a special case. All transistor circuits have a linear range where the output current is a linear function of the base current/gate voltage. In other words, if we were to drive a simple emitter-follower amplifier with a low level sine wave, the output waveform will look just like the input waveform. At high input level, the output will be distorted, just like the case of the sine wave shown above.

The same applies to nearly all integrated circuits that take some input into CMOS logic due to these characteristics of transistors. In contrast, a linear IC operates over a continuous range of input levels and has an output proportional to its inputs. Amplifiers are interesting in that they are sometimes nonlinear devices and sometimes linear devices in electronics. Let's look at this more closely...

## Nonlinearity in Amplifiers

Amplifiers are interesting because they have a certain range where they purport to be perfectly linear. This is not exactly true for power amplifiers that are intended for use with FM signals, which have a specification called IP3 (third-order intermodulation intercept point) that basically measures how much distortion can arise in the time-domain waveform.

When we look at the voltage transfer curve for an op-amp, two regions of operation become apparent. In the linear region, the output changes linearly with respect to the input. The large slope of the line indicates that the relationship between the output voltage and input voltage. In the non-linear or saturation region, the input voltage has very little impact on the output voltage.

Basic operational amplifiers function as a three-stage high gain amplifier that amplifies, filters, sums, and buffers analog signals. A differential amplifier usually works as the first stage of the amplifier while the next stage develops a large voltage gain. With the final stage working as a class B voltage follower, an op-amp has a high input impedance, a low output impedance, and a high voltage gain. Op-amps use negative feedback to eliminate distortion caused by non-linear transistors.

Referring to the basic diagram, op-amps have a minimum five terminals with the positive and negative supply voltage terminals located at +V and –V. One input produces an inverted output signal while the other input produces a non-inverted output signal. The inverting input terminal has a negative designation while the non-inverting input terminal has a positive designation. The point of triangle points in the direction of the signal flow and connects to the output terminal.

We can use a basic operational amplifier to explore the linear range of linear integrated circuits. When an op-amp operates in the linear region, the -mode input voltage reaches its maximum value. The positive and negative supply voltages define the input mode and output mode swing ranges and the output voltage of the amplifier. In the linear range, the input and output signals remain within the input -mode and output -mode swing ranges.

## Examine Linear and Nonlinear Circuits With Simulations

Circuit simulations are the best way to examine the linear and nonlinear ranges of different circuits before you start your PCB layout. In particular, SPICE simulations will let you look in the time-domain to spot when distortion occurs as an input signal level increases. You can also do DC simulations with a SPICE simulator, which lets you identify when the nonlinear threshold for a component is reached. Using parameter sweeps with DC or AC simulations also gives you a simple way to check how a circuit's nonlinear behavior is affected by component values.

The complete set of circuit design tools in Altium Designer^{®} give you access to a powerful and intuitive SPICE-based simulator for linear devices in electronics and for common nonlinear circuits. Altium Designer includes built-in libraries with standard simulation models, and you can access an additional range of components through Altium Concord Pro on the Altium 365^{®} platform. If you're working with specialty components or you are using custom simulation models, you can import these models into your circuit designs and examine signal behavior with Altium Designer's simulation toolset.

We have only scratched the surface of what is possible to do with Altium Designer on Altium 365. You can check the product page for a more in-depth feature description or one of the On-Demand Webinars. Talk to an expert at Altium today to learn more.