# How to Measure Impedance Using the Circuit Impedance Formula

Impedance affects the propagation of signals via a circuit board. Also, it affects the exchange of power between components and the leakage of signals in undesired parts of a circuit board. The impedance of a circuit can be determined in several methods. However, these methods don’t provide realistic results until proper parasitic elements are included in the models.

## What is the Importance of Impedance Matching in a Circuit Board?

The traces of circuit board function as transmission lines with certain impedance values at every point. Also, impedance matching remains constant at every point all through the trace.

An impedance that fluctuates in a transmission line causes signal reflection to disturb signal integrity. Controlled impedance is crucial as it ensures signals don’t degrade as they propagate via the trace.

## Methods of Calculating the Impedance of a Circuit

You can calculate the impedance of a circuit by using different methods.

Online calculators

With the help of online calculators, you can determine the impedance of a circuit. An impedance calculator integrates Maxwell’s equations for circuit board transmission lines. This calculator generates data that are suitable and accurate for PCB manufacture. Also, this tool gives an estimate of trace parameters like effective dielectric constant of the structure, capacitance, and propagation delay for each unit length.

Circuit simulation

This technique confirms the functionality of a PCB design before manufacturing begins. Most PCB design software applications now include impedance calculation. One of the main benefits in this place is that you can modify impedance design parameters to carry out different simulations. Once you carry out the simulations, you can select the best PCB design.

Practical method

This is a practical way of calculating the impedance of a circuit. To arrive at the circuit impedance formula, you need to calculate the rise time for the trace.

Tr=0.35/fmax

fmax represents the maximum operating frequency

After calculating the rise time for the grace, you will calculate the maximum trace length

I=tr x 2 in/ns

Therefore, the circuit impedance formula will be

Z= √(R2 + (XL – XC)2)

## Factors that Determine the Impedance of a PCB

The arrangement of components on a circuit board determines the impedance of a circuit. A circuit impedance depends on the inner conductive planes and the PCB substrate. The impedance of a circuit board is determined by several factors.

Transmission line impedance

A number of impedance values can characterize the impedance of transmission lines. However, the characteristic impedance determines the impedance of a transmission line. The characteristic impedance is a transmission line’s impedance in complete isolation. There are other metrics that quantify transmission line impedance. These are odd and even mode impedances.

Odd mode refers to a transmission line impedance when you operate two traces in a pair differentially. Even mode describes the transmission line impedance when you operate two traces in a pair evenly.

Board stackup and material selection

Stackup simply refers to the arrangement of PVB materials in order. The conducting layers in a board stack up can cause a parasitic effect which influences a circuit impedance. Also, there will be reflections on the traces if impedance mismatch is a result of parasitic. This will eventually cause EMI or crosstalk issues.

Furthermore, stack-up reveals your expectations to the manufacturers. It is also important you select a suitable substrate material. This is because the Dk of your substrate will impact the geometry needed to produce a transmission line with a particular impedance.

Via impedance

Vias in a multilayer circuit will have some parasitic between conductive elements. The inductance of a via depends on its aspect ratio. Also, via impedance ranges between 25 to 35 ohms. Therefore, there is a difference between via impedances and trace impedances. When you place a via hole on conductive traces, there will be noise coupling and this will result in impedance discontinuities in the long run.

## How to Measure and Analyze Impedance in a Circuit

You can measure circuit impedance using a setup that comprises oscilloscope, the load with impedance, and a signal generator. Also, you will need to analyze the phase shift and output amplitude against the particular frequency’s input signal. Equipment such as impedance analyzers and impedance meters are ideal for measuring impedance.

However, these measures can only be applied when there is a finished circuit board. You will need to make use of analytical and simulation tools to measure a circuit impedance if you are designing a circuit. The SPICE-based simulator can help you to measure the impedance of a linear circuit by integrating an AC frequency sweep.

Non-linear circuits require the integration of advanced analyses. A DC sweep is the best tool for non-linear circuits. This is because it explains how a DC input voltage propagates a current and an output voltage. Also, make use of small-signal analysis when you are working around AC signals. The harmonic balance analysis is another powerful technique. This  analysis reveals the sinusoidal signal.

What Causes Instability when Measuring Impedance?

Since there are different methods of measuring circuit impedance, there may be discrepancies in the values. Below are the causes of instability when measuring impedance

Measurement environment: Various conditions affect impedance measurement. This includes the temperature of resistors, capacitors, and inductors.

Parasitic components: Components with parasitic components can result in instability of the measure values.

What Factors Affect Controlled Impedance?

The dimensions of the trace which includes trace thickness and trace width, dielectric thickness of the PCB material, and the dielectric constant determine the impedance of a trace. The trace impedance is usually within the range of 25 and 125 Ohms. Below are factors that affect the impedance of PCB trace

• The core material’s thickness
• Dielectric constant of the prepreg and core material
• Thickness and width of the copper signal trace

Controlled impedance is crucial for high-speed applications like RF transmission and telecommunication.

## Conclusion

Measuring the impedance of a circuit is crucial in determining the functionality of such circuit. Impedance determines a lot of parameters in circuit boards. The circuit impedance formula helps to determine the impedance value of a circuit.

Get Fast Quote Now