Role of Impedance Equation in High Speed Designs

Impedance is one of the most important ideas that controls how signals behave in systems. Signal integrity issues arise from reflections in the signal caused by impedance mismatches. To guarantee that there is no signal loss, reflection, or distortion, engineers must carefully control impedance. The resistance of an electric circuit to the application of alternating current is measured by its impedance. It is the result of combining high-frequency induction and capacitance in an electric circuit. Like resistance, impedance is measured in ohms. Different impedances cause attenuation and reflections, which weaken the signal. The definition of impedance, its differences from other circuit factors such as resistance, inductance, and capacitance, and the significance of its equation for high-speed PCB design are all covered in this article.

Impedance vs Resistance, Inductance, and Capacitance

Impedance is the total equivalent resistance that prevents current from flowing through circuits that contain resistors, inductors, and capacitors. Reactive and resistive components make up impedance. The energy in a circuit is released as heat by resistors. The electromagnetic fields that surround and penetrate conductors, inductors, and capacitors in a circuit contain the recoverable energy.

Depending on the circuit architecture and frequency, impedance combines all of these features. Inductance and capacitance only play a role in AC circuits. But resistance influences both DC and AC circuits. The following parts provide the equation and diagram depiction.

What is Impedance?

The symbol Z stands for impedance, which is the amount of resistance an AC circuit poses to its flow. It contains both reactive (imaginary) and resistive (actual) components. Impedance changes with frequency because of inductance and capacitance. Whereas resistance opposes current consistently. Like resistance the impedance is also measured in ohms (Ω), but it also includes phase shift and frequency dependency.

The general formula for impedance in an AC circuit is:

Z = R + jX

• R is resistance,
• X is reactance (which can be inductive or capacitive),
• j is the imaginary unit (√-1), and
• ω (omega) is the angular frequency (2πf)

Here, jw (or jω) represents the frequency-dependent component of the impedance. It signifies that the impedance changes with the signal's frequency due to the reactive components. The reactance part can be further expanded as:

• For an inductor: Xl = ωL = jwL
• For a capacitor: Xc = -1/ωC = -j/(wC)

The Triangle of Impedance

In a vector diagram, impedance is often represented as a triangle:

• The horizontal axis shows resistance (R)
  The vertical axis shows reactance (X)
• The hypotenuse represents the magnitude of impedance (|Z|)

Helps in visualizing how the total impedance is due to resistance versus reactance.

Factors Affecting Impedance in PCB Design:

What is Characteristic Impedance?

Characteristic impedance (Z0) refers to the impedance of a transmission line. It exhibits when it is infinitely long or properly terminated. It remains constant regardless of the trace length as long as the cross-sectional and dielectric properties remain the same. A sudden change in impedance causes part of the signal to reflect back. This is vital for designing transmission lines that carry high-speed digital signals without reflections. It can corrupt data integrity. It is not influenced by length but determined by the geometry and materials of the PCB trace:

Z0 = √((R + jωL)/(G + jωC))

In practical high-speed PCB designs, R and G (conductance) are often negligible, so it simplifies to:

Z0 ≈ √(L/C)

Characteristic impedance is typically set at standard values like 50Ω (single-ended) or 100Ω (differential). And sometimes for USB differential pair data routing the value is taken 90Ω.

Using JLCPCB Impedance Calculator:

Launch the "Impedance Calculator" in JLCPCB, choose the appropriate layer stack-up, and enter the impedance values along with other pertinent data such board thickness. In your engineering data, create the appropriate line width and spacing.

Important Manufacturer's Note: Our factory will manage the impedance within a tolerance of ±10% for orders with "Impedance Control" chosen as "Yes." Selecting "No" will not allow us to regulate the impedance, but we will make sure that the line width and spacing are within a +/-20% tolerance. Double-sided boards do not currently have impedance control.

Conclusion

A key component of high-speed PCB design is the impedance equation. Knowing the formation, calculation and measurement of impedance. This will lessen jitter and assist engineers preserve signal integrity. In order to attain the intended impedance values and expedite the design process, impedance-controlled lines and tools such as JLCPCB's Impedance Calculator can be used.

The optimum value you determined from a schematic may not match the impedance signals seen on an actual PCB layout. The existence of the substrate and the tracing layout of the board are the primary causes of this. Crosstalk is one effect of this that deviates from the ideal impedance levels. Circuits that switch at high frequencies may experience problems with power integrity, such as ringing. The impedance of your power delivery network will also deviate from the ideal capacitive behavior at higher frequencies, which could lead to problems with both power and signal integrity.