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The Sierra Circuits Impedance Calculator uses the 2D numerical solution of Maxwell’s equations for PCB transmission lines. It renders fairly accurate results suitable for use in circuit board manufacturing and engineering analysis. In addition to characteristic impedance of a transmission line, the tool also calculates line parameters such as capacitance, inductance, propagation delay per unit length, effective dielectric constant of the structure, and in the case of differential pairs, coupling coefficient, and even & odd mode characteristic parameters. Most of the free online tools for impedance calculations are generally not as accurate as they are based on empirical formulas and do not take into account the trace’s trapezoidal shape or the effect of multiple dielectric materials.

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Impedance between two points in an electronic circuit can be defined as the ratio of the voltage difference and the current. It is the AC voltage difference between the two points divided by the AC current. It is assumed here that the AC voltage and currents are sinusoidal with a frequency ‘f’ cycles/sec (the radian frequency, ω, equals 2πf radians/sec). In general, impedance is a function of frequency. The unit of impedance is Ohms (Ohm= volt/ampere).

For a pure resistor of resistance R Ohms, the impedance ZR = R Ohms.

For a pure inductor of inductance L Henries, the impedance ZL= jωL Ohms.

For a pure capacitor of capacitance C Farads, the impedance ZC = 1/jωC Ohms.

Impedances can be combined in series and parallel in the same manner as resistors.

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Signals propagate on a transmission line as electromagnetic waves with a propagation speed and attenuation factor per unit length. Between any point on the signal line and the corresponding point on the signal return path, the instantaneous AC voltage and the instantaneous AC current are related as follows:

Impedance of the transmission line at that point=instantaneous AC voltage instantaneous AC current

This impedance is referred to as the characteristic impedance of the transmission line. If the transmission line has the same characteristic impedance along its length, it is called a uniform transmission line.

On a transmission line, whenever a propagating signal encounters a change in characteristics at any point, some part of the signal will be reflected and signal distortion will occur. Therefore, in order to have good signal integrity, it is important to have a uniform transmission line with the characteristic impedance at every point.

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A PCB transmission line comprises a signal trace and its return path- usually the nearest reference plane(s). If the geometry of the signal trace, its return path, and the material between them is unchanged throughout the length of the trace, then we have a uniform PCB transmission line. A uniform transmission line will have the same characteristic impedance along its length. Taking into account the manufacturing considerations, achieving a reasonably uniform transmission line is termed as a controlled impedance line, and its characteristic impedance is also referred to as controlled impedance.

When high-frequency signals propagate on transmission lines, a uniform controlled impedance is critical to achieve signal integrity, that is the transmission of the signal without distortion. Typically, you will need controlled impedance lines for high-speed digital and high frequency RF/microwave applications.

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Impedance of circuit board traces is determined by:

• Trace width and thickness
• Height of the dielectric layer between the signal trace and the reference planes
• Dielectric constant(s) of the dielectric material used in the board
• Spacing between differential pair traces

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PCBs typically use two types of transmission line structure: microstrip and striplines. There are 3 types of microstrip models to choose from- uncoated, coated, and embedded. Each of the transmission lines consists of a signal trace and a reference plane(s). Within each model, the following combinations are available:

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An uncoated microstrip structure consists of a signal trace on an outer layer of a PCB. The reference layer is typically the next layer above or below the signal layer trace. Uncoated microstrips do not have a soldermask coating above the trace.

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A coated microstrip structure consists of a signal trace on an outer layer of a PCB. The reference layer is typically the next layer above or below the signal layer trace. Coated microstrips have a soldermask coating above the trace.

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An embedded microstrip is a structure similar to a traditional microstrip, except there is an extra dielectric layer above the signal trace. Embedded microstrips can be designed on the internal layers of a circuit board.

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A stripline is a structure composed of a uniform signal trace on an inner layer of a board. It is separated by a dielectric layer followed by copper planes on each side.

Our impedance calculator features two main types of impedance models, single ended and differential, within each trace structure.

• There are 3 types of single ended models- single ended, coplanar single ended, and coplanar single ended without ground.
• There are also 3 types of differential models- differential, coplanar differential, and coplanar differential without ground.

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Following is the table of 82 impedance calculators that are designed and categorized based on the different trace geometries:

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Choose the right impedance calculator mode based on the geometry of the signal layer and the relevant reference plane(s).

The previously mentioned trace geometries have been drawn based on where the traces are routed and on which layer they are present. Whether the traces are embedded in between layers or on the surface of the circuit board, designers can easily choose the right type of calculator to suit their design needs.

If you know the target impedance, the trace width can be calculated immediately.

Just enter the desired impedance in the ‘Target Impedance’ tab and hit the ‘Calculate’ button provided alongside the ‘Trace Width’ tab.

If you know the target trace width, the impedance can be calculated immediately.

Insert the known trace width in the ‘Trace Width’ tab and hit the ‘Calculate’ button provided alongside the ‘Calculated Impedance’ tab.

Calculate accurate impedances for PCB models having different dielectrics.

PCB models that use different dielectric materials to achieve the desired impedance accuracy have been earmarked as composite models ‘A’, ‘B’, and ‘C’. The impedance calculator features composite geometry where the traces are embedded between different dielectric materials having different height and dielectric constants to achieve accurate impedance values.

• Composite model A : In this model, we have used two different dielectric materials at the bottom.

• Composite model B: Here, you can find two different dielectric materials on the top.

Composite model C : In model ‘C’, two different dielectric materials can be found both on the top and bottom.

Note: These composite models are also available for single-ended, differential pair, and coplanar configurations.

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The dielectric that is closer to the trace has more effect on the trace’s impedance than the dielectrics that are afar. Composite geometry is most useful when multiple dielectric layers are present with different dielectric constants (Er). Instead of calculating effective dielectric constant, composite models allow us to use the parameters as it is to get more accurate impedance values. So, composite models are more practical in obtaining precise impedances than their non-composite counterparts.

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Default input parameters

• Dielectric height (H): The height of the dielectric material above or below the trace.
• Dielectric constant (Er): Dielectric constant of the dielectric material above or below the trace.
• Trace width (W)
• ΔW: The difference in width between the top and bottom of a trace. This difference is based upon the copper used on that layer, including plating.

•  Trace thickness (T): Determined by the copper weight used on that layer. For example, a trace on a 0.5 oz layer would have a trace thickness of 0.7 mils, and a trace on a 1 oz layer would have a trace thickness of 1.4.
• Target Impedance (Zo) for single-ended/differential

Default output parameters 

• Calculated impedance (Zo) for single-ended/differential
• Propagation delay (Pd): Propagation delay on a PCB trace is the one-way (source to load) time required by a signal to travel on that trace. It is expressed in time per unit length. Propagation delay is the function of the dielectric constant (Er) and the trace geometry/structure.
• Inductance (Lo)
• Capacitance (Co)
• Effective dielectric constant (Ereff): When different dielectrics are used, an effective dielectric constant is calculated based on the ratio between actual capacitance with actual dielectrics and the capacitance when the dielectrics are replaced by air.

Additional parameters for complex differential design needs

• Trace inductance (L1S)
• Mutual inductance (Lm)
• Trace capacitance (C1S)
• Mutual capacitance (Cm)

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The units can be changed as per your requirement. You can take the print out of your final readings by clicking the ‘print’ button.

The impedance calculators are ideal for high-speed traces that require specific impedance for lossless data transfer. You need to understand your PCB design to get the most out of it. You can also check out our HDI PCB Stackup Designer tool if you are facing problems with your stack-up.