Impedance standard: Impedance, defined as the ratio of AC voltage to current, is known as the active definition of impedance. Alternatively, impedance is also an intrinsic property of materials and substances, whose magnitude can be calculated based on their geometric shape and the electromagnetic characteristics of the surrounding space—this is referred to as the passive definition of impedance. The latter approach, being directly tied to fundamental physical quantities, is particularly well-suited for establishing metrological standards.
Introduction
Impedance is a parameter that depends on the circuit's structure. In circuits containing resistors, inductors, and capacitors, the opposition to the flow of current is referred to as impedance. Impedance is commonly represented by the symbol Z and is a complex quantity: its real part is called resistance, while its imaginary part is known as reactance. Impedance essentially represents the vector sum of resistance and reactance. Specifically, the opposition offered by a capacitor to alternating current in a circuit is called capacitive reactance, whereas the opposition provided by an inductor to AC is termed inductive reactance. Together, the effects of capacitance and inductance on AC signals within a circuit are collectively referred to as reactance. The unit of impedance is the ohm.
In an electric current, the opposition that a material offers to the flow of electricity is called resistance. With the exception of superconductors, all materials in the world have some level of resistance—though the actual values vary widely. In both direct current (DC) and alternating current (AC), resistance acts as a hindrance to the flow of both types of electricity. However, when it comes to common electronic components like capacitors and inductors, their behavior toward DC and AC differs significantly from that of resistors. While resistors block both DC and AC equally, capacitors exhibit a unique property: they "block DC while allowing AC to pass." In other words, DC cannot flow through a capacitor, whereas AC can—and the higher the capacitance value or the frequency of the AC signal, the less the capacitor resists the flow of AC. This opposition to AC can indeed be described using the concept of "resistance," but it’s important to note that it’s not exactly the same as ordinary resistance. Instead, this phenomenon is referred to as "reactance." Reactance shares the same unit as resistance, and together, they are collectively known as "impedance."
Introduction to Input and Output Impedance
Input impedance
Input impedance refers to the equivalent impedance at the input terminal of a circuit. If you connect a voltage source U across the input terminals and measure the resulting current I, the input impedance Rin is simply U/I. You can think of the input terminals as the two ends of a resistor—where the resistance value of that resistor equals the input impedance.
The input impedance is no different from that of a typical reactive component—it simply reflects the extent to which it resists current flow. In voltage-driven circuits, a higher input impedance means a lighter load on the voltage source, making it easier to drive and minimizing any impact on the signal source itself. Conversely, in current-driven circuits, a lower input impedance results in a lighter load for the current source. Thus, we can summarize: if the circuit is driven by a voltage source, maximizing input impedance is ideal; but if it’s driven by a current source, minimizing impedance is preferable. (Note: this principle applies primarily to low-frequency circuits—high-frequency designs also require careful consideration of impedance matching.) Additionally, when aiming for maximum power transfer at the output, impedance matching becomes a critical factor to consider.
Output impedance
Whether it's the signal source, amplifier, or power supply, all of them face the issue of output impedance. Output impedance essentially refers to the internal resistance of a signal source. Ideally, an ideal voltage source—such as a power supply—should have zero internal resistance, while an ideal current source should exhibit infinite impedance. Output impedance is something that requires particular attention during circuit design.
However, real-world voltage sources cannot achieve this perfectly. Instead, we often model an actual voltage source by connecting an ideal voltage source in series with a resistor \( r \). This resistor \( r \), connected in series with the ideal voltage source, represents the internal resistance of the (signal source/amplifier output/power supply). When this voltage source supplies power to a load, a current \( I \) flows through the load and creates a voltage drop of \( I \times r \) across the resistor. As a result, the output voltage of the power source decreases, which ultimately limits the maximum available output power. (For more on why this limits the maximum output power, refer to the following question on "impedance matching.") Similarly, an ideal current source should have infinite output impedance—but in practice, such a configuration is simply impossible to realize.
Classification and Measurement of Impedance
Depending on the frequency and circuit configuration, impedance is classified into lumped-parameter impedance and distributed-parameter impedance.
When the frequency is low, the size of circuits and components becomes very small compared to the wavelength, allowing the circuit to be modeled as a collection of lumped-parameter elements such as individual resistors, capacitors, and inductors. However, as the frequency increases—and especially at high frequencies—all circuit components must be treated as uniformly distributed across every point in the circuit, with impedance now manifesting as distributed-parameter impedance.
Methods for measuring lumped-parameter impedance include the voltmeter-ammeter method, the bridge method, and the resonance method, among others.
Impedance Standard
Lumped-parameter impedance standard
Typically, a high-frequency capacitance standard is used—essentially a short, tightly packed coaxial air-dielectric transmission line. Its value can be directly calculated from the line's geometric dimensions and the relative permittivity of air. By employing various null or resonant-type instruments, along with direct comparison and extrapolation techniques, this value can then be transferred to various working standards for lumped-parameter impedance measurements.
Microwave Impedance Standard
Refers to physical standards corresponding to microwave impedance-related quantities such as characteristic impedance, impedance, voltage reflection coefficient, and voltage standing wave ratio. Commonly used are characteristic impedance standards and reflection coefficient standards (also known as standard loads).
Feature Resistance Standard
There are two standard types: coaxial cable and waveguide. The former is a rigid, air-insulated coaxial line without dielectric support; the latter is a precisely machined section with standardized cross-sectional dimensions, secured by flanges to meet industry standards. Both types have characteristic impedances calculated based on their geometric dimensions—and these impedances are rigorously maintained through precision machining.
Reflection Coefficient Standard
The reflection coefficient standard, also known as the standard load, is categorized into three types: ① Standard large-reflection loads include devices such as 1/4-wavelength short-circuited stubs, shorting plates, shorting pistons, and coaxial open-circuit terminations. ② Standard mismatched loads are characterized by mismatched standing-wave ratios ranging from 1.05 to 2.0. ③ Standard non-reflective loads consist of matched loads and similar components. Additionally, based on their structural design, these loads can be further divided into fixed and sliding types. The sliding type is most commonly implemented as a small-reflection standard.