How to Perform Linearity Circuit Analysis

January 28, 2021 Cadence PCB Solutions

Key Takeaways

  • Understand the concept of circuit linearity.

  • Learn how to perform linearity circuit analysis.

  • Determine if AC-driven circuits are linear.

I’ve had a phobia of blowing up balloons, ever since one blew up in my face as a kid. While it’s easy to expand the balloon by blowing more air into it, it’s difficult to estimate when to stop before it ultimately pops. 

It’s similar to when current and voltage are placed in a circuit—it’s critical to know their relationship and how they will affect the performance of the circuit. This is why understanding circuit linearity and performing linearity circuit analysis is important during the PCB design process. 

What Is Circuit Linearity?

Before you can conduct a linearity circuit analysis, you need to understand circuit linearity. In electronics, a linear circuit consists of elements within a resistor that result in a proportional relationship between voltage and current. 

Resistors are considered to be a linear element. When placed in a circuit, the flow of current through the resistor changes proportionately to the voltage that falls across it. The relationship between voltage and current can be expressed in a linear equation of ax + b = 0. Inductors and capacitors are also considered linear elements.

Linear I-V relationship of a resistor

The relationship between voltage and current in a resistor.

What about a non-linear circuit? How does it react to current changes? This type of circuit is made up of one or more non-linear components, which does not satisfy the linear equation. Changes made to one parameter is not proportionately reflected in another parameter. The diode is a good example. 

Non-linear diode current flow

Non-linear I-V curve of a diode.

Consider the above I-V chart of a diode. When driven in forward-bias, no current flows between 0V to the junction voltage, which is around 0.7V for silicone. Once the voltage exceeds the junction voltage, the current rises dramatically. 

The diode also demonstrates non-linearity when driven in reverse bias configuration, with a small amount of leakage contrasted by the large breakdown current. Other non-linear elements include transistors, transformers, and SCR. 

Linear circuits are solvable for any time constant. However, non-linear circuits have many solutions or no solutions at all. 

Performing Linearity Circuit Analysis

Analyzing a linear circuit requires basic electronics knowledge, particularly in Ohm’s Law and Kirchoff’s Laws. Ohm’s Law defines the relationship of voltage, current, and resistor with the following formula:

V = IR

When any two of the parameters are known, the third one can be calculated. 

Often, a linear circuit consists of many elements that are either in series, parallel, or a combination of both. This is when Kirchoff’s Laws become useful. The first Kirchoff Law, or Kirchoff’s Current Law, states that the total current entering the node is equal to the amount leaving it.

Visual representation of Kirchoff’s Laws

Kirchoff’s Voltage and Current Laws

Meanwhile, the second Kirchoff Law, or Kirchhoff's Voltage Law, states that the sum of all potential differences in a closed loop is equal to zero. By using both Kirchoff Laws, you can solve complex linear circuits by establishing the equations for each of the subcircuits. 

Here’s an example.

Parallel-series linear circuit showing resistance

Example of a linear circuit.

The above circuit consists of resistors arranged in parallel-series configuration. When the voltage and resistance are known, the current flowing to each loop can be calculated.

According to KVL, two equations for each loop can be defined as such:

Vcc = I1 (R1 +R2 + R4)  (eq 1)

Thus, I1 and I2 can be solved as follow: 

I1 = Vcc / (R1 +R2 + R4)

Applying KCL, It is known by the following equation.

It = I1 + I2.

Are AC-Driven Circuits Linear?

Often, AC-driven circuits can be mistaken as non-linear as the basis that determines the linearity of a circuit is the relationship between the voltage and current. While an AC signal varies with time, it still exhibits a linear relationship across elements like resistors, capacitors, and inductors. Therefore, AC driven circuits are linear. 

While linearity circuit analysis is considerably straightforward, the calculations can be tedious when you have layers of nested subcircuits. You’ll save precious time with the right software. Cadence PSpice Designer is a complete front-to-back design tool, enabling fast and efficient circuit analysis



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