What is Impedance?

Impedance, represented by the symbol Z, is a measure of the total opposition that a circuit presents to alternating current (AC). It is similar to resistance, but whereas resistance opposes the flow of direct current (DC), impedance opposes the flow of alternating current. Impedance is measured in ohms (Ω).

Impedance consists of two components:
– Resistance (R) – opposes current flow and dissipates energy as heat
– Reactance (X) – stores energy in electric or magnetic fields and returns it to the circuit

Reactance can be either inductive (X_L) or capacitive (X_C). Inductive reactance resists changes in current, while capacitive reactance resists changes in voltage.

The total impedance Z of a circuit with resistance R, inductive reactance X_L, and capacitive reactance X_C is given by:

Z = R + j(X_L – X_C)

where j is the imaginary unit equal to √-1. This shows that impedance is a complex quantity with both real (resistive) and imaginary (reactive) parts.

Impedance in Transmission Lines

In the context of electrical transmission lines, impedance takes on special importance. The Characteristic Impedance Z₀ of a transmission line is determined by the inductance L and capacitance C per unit length of the line:

Z₀ = √(L/C)

For a lossless line, the characteristic impedance is purely real. However, real transmission lines have some resistance, so the characteristic impedance is complex with a small imaginary part.

When a transmission line is terminated with a load impedance Z_L equal to its characteristic impedance Z₀, the line is said to be matched. A matched line has no reflections and maximum power transfer to the load.

If the load impedance differs from the characteristic impedance (i.e. Z_L ≠ Z₀), then some of the incident wave is reflected back toward the source. The amount of reflection is given by the reflection coefficient Γ:

Γ = (Z_L – Z₀)/(Z_L + Z₀)

The reflection coefficient is a complex number with magnitude between 0 and 1. A reflection coefficient of 0 indicates no reflection (matched load), while a coefficient of 1 indicates total reflection (open or short circuit). The power reflected is proportional to |Γ|².

Defined Impedance

A transmission line or connection with a specific, consistent characteristic impedance is said to have defined impedance or controlled impedance. The most common characteristic impedances are 50Ω, 75Ω, and 110Ω, but other values are used in certain applications.

There are several reasons why defined impedance is important:
1. Impedance matching – As explained above, matching the load impedance to the line’s characteristic impedance minimizes reflections and maximizes power transfer. This is critical for applications like radio frequency (RF) systems and high-speed digital lines.
2. Consistency – Having a consistent, defined impedance makes it easier to design circuits and systems. Transmission line segments with the same characteristic impedance can be treated as simple building blocks.
3. Interoperability – Using standardized impedances like 50Ω and 75Ω allows different devices and components to work together seamlessly. Connectors, cables, and PCB traces can be designed for a specific impedance.
4. Signal integrity – Maintaining controlled impedance helps preserve signal integrity by minimizing reflections, ringing, and distortion. This is especially important for high-frequency signals and fast digital pulses.

Impedance Control in PCBs

Printed circuit boards (PCBs) are a common place where controlled impedance is essential. High-speed digital traces, RF transmission lines, and analog signals all depend on consistent, defined impedance to function properly.

There are several PCB design techniques used to achieve controlled impedance:
– Trace width and spacing – The width of the trace and its spacing from neighboring traces and planes affect the characteristic impedance. Wider traces have lower impedance, while narrower traces have higher impedance.
– Dielectric thickness – The thickness of the dielectric material (e.g. FR-4) between the trace and the reference plane affects impedance. Thicker dielectrics result in higher impedance.
– Reference planes – Having uninterrupted reference planes (ground and/or power) beneath or adjacent to the signal trace helps control the impedance.
– Differential pairs – Differential signaling uses two traces with equal and opposite signals. The traces are routed close together with a specific spacing to achieve the desired differential impedance.

PCB manufacturing can include controlled impedance as a special process. The manufacturer adjusts the trace width, spacing, and dielectric height to achieve the specified impedance within a certain tolerance (e.g. ±10%). This requires careful control of the PCB Stackup materials and dimensions.

Some common controlled impedances for PCBs include:
| Impedance | Application |
|———–|——————————————-|
| 50Ω | RF circuits, test equipment, coaxial cable |
| 75Ω | Video, cable TV, some RF |
| 90Ω | Differential USB, Ethernet |
| 100Ω | Differential LVDS, ECL, PECL |
| 110Ω | Twisted pair Ethernet |

Measuring Impedance

To verify that a transmission line or PCB trace has the expected characteristic impedance, it needs to be measured. There are several instruments and techniques for measuring impedance:
– Time-domain reflectometer (TDR) – A TDR sends a fast rise time pulse down the line and measures the reflections. From the amplitude and timing of the reflections, the impedance profile along the line can be determined. TDR is the most common method for measuring Controlled Impedance PCBs.
– Vector network analyzer (VNA) – A VNA measures the frequency response of a network, including the impedance. By sweeping the frequency, the VNA can determine the impedance at each frequency. VNAs are often used to characterize RF components and circuits.
– Impedance analyzer – An impedance analyzer directly measures the impedance and phase angle of a component or network at a single frequency or a range of frequencies. They are used for general impedance measurements, especially for non-transmission line circuits.
– Resistive divider – For purely real (resistive) impedances, a simple Voltage Divider can be used to estimate the impedance. The unknown impedance forms one leg of the divider, and the voltage ratio indicates the impedance ratio. This method is not suitable for reactive or frequency-dependent impedances.

Regardless of the measurement method, it’s important to use proper techniques to get accurate results. The test setup should use cables and connectors with the same characteristic impedance as the device under test (DUT). The measurement reference plane should be calibrated to the end of the test cable or probe. Averaging multiple measurements can help reduce noise and uncertainty.

Applications

Defined impedance is critical in many applications spanning electronics, telecommunications, and related fields. Some examples include:
– Radio frequency (RF) circuits – Impedance matching is vital in RF systems to maximize power transfer and minimize reflections. Components like antennas, filters, and amplifiers are designed for specific impedances, usually 50Ω or 75Ω.
– High-speed digital – As data rates increase, the fast edges of digital signals interact with the transmission line impedance. Controlled impedance PCBs are used to maintain signal integrity and minimize reflections, crosstalk, and EMI.
– Telecommunications – From long-haul fiber optic links to the last mile of twisted pair cable, the telecommunications network relies on defined impedances. For instance, Category 5 Ethernet cable has a nominal impedance of 100Ω, while RG-6 coaxial cable used for cable TV has a 75Ω impedance.
– Audio and video – Analog audio and video signals are transmitted over coaxial cables with defined impedances to preserve quality. Professional video often uses 75Ω BNC connectors, while consumer audio typically uses 75Ω RCA connectors.
– Automotive – Modern vehicles have an increasing number of high-speed data links for communications, infotainment, and driver assistance systems. Controlled impedance is essential for the reliability of these mission-critical networks.
– Aerospace – Avionics systems and satellite payloads use controlled impedance interconnects to ensure signal integrity in harsh environments. Light weight and tight tolerances are key requirements in these applications.

As technology advances, the use of defined impedance will continue to expand. Higher frequencies, faster data rates, and denser circuits will require even tighter impedance control to maintain performance and reliability.

Frequently Asked Questions (FAQ)

1. What is the difference between impedance and resistance?
   Impedance is the total opposition to alternating current (AC), while resistance is the opposition to direct current (DC). Impedance includes both resistance and reactance, and is a complex quantity with magnitude and phase. Resistance is purely real and has no phase component.

2. Why is 50Ω a common characteristic impedance?
   50Ω is a good compromise between power handling and signal loss. Lower impedances have less voltage drop and power loss, but require thicker conductors. Higher impedances allow thinner conductors, but have more signal attenuation. 50Ω provides a balance of these factors and has become a standard impedance for RF systems, test equipment, and coaxial cables.

3. What happens if a transmission line is not terminated in its characteristic impedance?
   If a transmission line is terminated with a load impedance different from its characteristic impedance, some of the energy is reflected back toward the source instead of being absorbed by the load. These reflections can cause signal distortion, ringing, and standing waves on the line. The severity of the effects depends on the magnitude of the impedance mismatch and the length of the line relative to the signal wavelength.

4. How does PCB trace geometry affect impedance?
   The characteristic impedance of a PCB trace depends on its width, thickness, and spacing from nearby conductors (e.g. ground or power planes). In general, wider and thicker traces have lower impedance, while narrower and thinner traces have higher impedance. The Dielectric Constant of the PCB material also affects the impedance. PCB design software can calculate the required trace dimensions for a given stackup and impedance.

5. Can impedance be measured with a multimeter?
   A standard multimeter can only measure DC resistance, not AC impedance. To measure impedance, you need an instrument that can apply an AC signal and measure the resulting voltage and current. Examples include impedance analyzers, LCR meters, vector network analyzers, and time-domain reflectometers. Some specialized multimeters have a built-in frequency generator for basic impedance measurements, but they are limited in frequency range and accuracy compared to dedicated impedance instruments.

Conclusion

Defined impedance is a critical concept in the design and analysis of electrical systems, particularly those involving transmission lines and high-frequency signals. By controlling the characteristic impedance of interconnects, designers can ensure proper termination, minimize signal distortion, and optimize power transfer.

This article has covered the basics of impedance, reflection, and transmission line theory, as well as the practical aspects of impedance control in PCBs and measurements. The FAQ section addressed common questions and misconceptions about impedance.

As digital systems continue to push for higher speeds and analog circuits move to higher frequencies, the importance of defined impedance will only grow. Designers and engineers in all fields of electronics must have a solid understanding of impedance to meet the challenges of advanced technologies.