What is Characteristic Impedance?

Characteristic impedance, also known as surge impedance or natural impedance, is a key property of transmission lines used in electrical and electronic systems. It is defined as the ratio of the voltage to the current for a wave propagating along the line.

The characteristic impedance (Z0) of a transmission line is determined by the geometry and materials of the conductors and the insulating medium surrounding them. It is expressed in ohms (Ω).

For a lossless transmission line, the characteristic impedance is given by:

Z0 = √(L/C)

where:
– L is the inductance per unit length
– C is the capacitance per unit length

Some key points about characteristic impedance:

• It is a fundamental property that determines how signals propagate along the line
• Matching the impedances of source, line, and load minimizes reflections and ensures maximum power transfer
• Mismatched impedances cause signal reflections, leading to distortion, loss, and interference
• Transmission lines are designed to have a specific Z0, typically 50Ω, 75Ω or 100Ω
• Characteristic impedance is frequency independent for lossless lines, but varies with frequency when losses are considered

Types of Characteristic Impedance

There are several types of characteristic impedance depending on the transmission line structure:

1. Coaxial Cable

Coaxial cables have a concentric construction with an inner conductor surrounded by an insulating dielectric and an outer conductor (shield). The characteristic impedance of a coaxial cable is given by:

Z0 = (138 / √εr) * log10(D/d)

where:
– εr is the relative permittivity of the dielectric
– D is the inner diameter of the outer conductor
– d is the outer diameter of the inner conductor

Common coaxial cable impedances are 50Ω (e.g. RG-58) and 75Ω (e.g. RG-6).

2. Twisted Pair

Twisted pair cables consist of two insulated conductors twisted together. They are commonly used for balanced transmission in applications like Ethernet. The characteristic impedance depends on the wire gauge, insulation properties, and twist rate.

Typical twisted pair characteristic impedances:
| Type | Impedance |
|——|———–|
| Cat 3 UTP | 100Ω |
| Cat 5/5e/6 UTP | 100Ω |
| Cat 7 S/FTP | 100Ω |

3. Microstrip

A microstrip transmission line has a conducting strip separated from a ground plane by a dielectric substrate. It is widely used in printed circuit boards (PCBs) for RF and high-speed digital applications.

The characteristic impedance of a microstrip line is approximated by:

Z0 = (87 / √(εr + 1.41)) * ln(5.98h / (0.8w + t))

where:
– εr is the relative permittivity of the substrate
– h is the substrate thickness
– w is the width of the microstrip
– t is the thickness of the microstrip

Typical microstrip impedances range from 20Ω to 120Ω, with 50Ω being very common.

4. Stripline

Stripline is another PCB transmission line structure where a flat conductor is sandwiched between two parallel ground planes. The characteristic impedance of a stripline is given by:

Z0 = (60 / √εr) * ln(4h / (0.67πw * (0.8 + t/h)))

where the variables have the same meaning as for microstrip.

Striplines offer better shielding and lower radiation than microstrip lines. They are often designed for 50Ω or 100Ω characteristic impedance.

Factors Affecting Characteristic Impedance

Several factors influence the characteristic impedance of a transmission line:

1. Conductor geometry: The shape, size, and spacing of the conductors determine the inductance and capacitance per unit length, which in turn affect Z0. Wider conductors and closer spacing lower the impedance.

2. Dielectric material: The insulating medium between the conductors affects the capacitance. Materials with higher dielectric constant (εr) result in lower characteristic impedance. Common PCB dielectrics like FR-4 have εr around 4.

3. Frequency: For transmission lines with loss, the characteristic impedance varies with frequency due to the skin effect and dielectric loss. The impedance increases with frequency, especially at high frequencies where losses are significant.

4. Surroundings: The presence of nearby conductors, ground planes, or enclosures can influence the characteristic impedance by altering the electromagnetic field distribution. Proper shielding and grounding techniques are important.

5. Manufacturing variations: Tolerances in conductor dimensions, dielectric thickness, and material properties can cause variations in the actual characteristic impedance compared to the designed value. Tight manufacturing controls are necessary for consistent performance.

Understanding and controlling these factors is crucial for designing transmission lines with the desired characteristic impedance and ensuring proper impedance matching in the system.

Frequently Asked Questions (FAQ)

1. What happens if the characteristic impedance is not matched?

If the characteristic impedance of a transmission line is not matched to the source and load impedances, signal reflections occur at the interfaces. These reflections cause a portion of the signal energy to be sent back towards the source, leading to loss, distortion, and potential interference with other parts of the system. Proper impedance matching is essential for maximum power transfer and signal integrity.

2. How do you measure characteristic impedance?

Characteristic impedance can be measured using a vector network analyzer (VNA) or a time-domain reflectometer (TDR). A VNA measures the impedance by analyzing the reflection and transmission coefficients of the line over a range of frequencies. A TDR sends a fast rise time pulse along the line and measures the reflected waveform to determine the impedance profile along the length of the line.

3. Can characteristic impedance change along a transmission line?

In an ideal lossless transmission line, the characteristic impedance is constant along the length of the line. However, in real lines with loss and manufacturing variations, the impedance can vary slightly along the line. Abrupt changes in impedance, such as those caused by connectors or discontinuities, can create significant reflections and degrade signal quality.

4. What is the effect of length on characteristic impedance?

The characteristic impedance of a transmission line is independent of its length. It is determined by the per-unit-length parameters (inductance and capacitance) which depend on the geometry and materials of the line. However, the overall impedance of the line (including any terminations) and the electrical length (phase shift) do depend on the physical length of the line.

5. How do you choose the right characteristic impedance for a design?

The choice of characteristic impedance depends on several factors such as the application, frequency range, available components, and system requirements. In RF and microwave systems, 50Ω is the most common choice due to compatibility with test equipment and standardized components. For high-speed digital designs, the impedance is often chosen to match the driver and receiver circuitry, typically 50Ω or 100Ω. Lower impedances allow for higher power handling, while higher impedances are better for voltage-sensitive applications. Simulation tools and reference designs can help in selecting the optimal impedance for a given design.