Input impedance is the total opposition a circuit presents to a signal at its input terminals, calculated as the ratio of voltage to current at that point. In its simplest form, it follows the generalized version of Ohm’s Law: Z = V / I, where both voltage and current are expressed as complex quantities to account for phase shifts caused by capacitors and inductors. The concept applies everywhere from basic resistor networks to transmission lines, amplifier circuits, and audio gear.
The Basic Formula: Voltage Over Current
For any circuit, input impedance is defined as the voltage across the input terminals divided by the current flowing into them. If you’re working with a purely resistive circuit (no capacitors or inductors), this is straightforward Ohm’s Law: R = V / I. Apply a known voltage, measure the current drawn, and divide.
When reactive components are involved, impedance becomes a complex number with both a real part (resistance) and an imaginary part (reactance). A capacitor’s impedance is 1/(jωC) and an inductor’s impedance is jωL, where ω is the angular frequency of the signal (2π times the frequency in hertz) and j represents the imaginary unit. For series combinations of resistors, capacitors, and inductors, you add these complex impedances directly. For parallel combinations, you use the reciprocal formula: 1/Z_total = 1/Z_1 + 1/Z_2 + … just as you would with parallel resistors, except now you’re working with complex numbers.
The magnitude of the complex impedance tells you how much the circuit resists current flow overall, while the angle (or phase) tells you how much the voltage leads or lags the current. Both matter when you’re designing circuits that need to pass signals cleanly between stages.
Measuring Input Impedance With a Voltage Divider
If you need to measure the input impedance of a device and can’t calculate it from a schematic, the voltage divider method is the most accessible approach. Place a known resistor (R_known) in series between your signal source and the device’s input. Then measure the voltage at the device’s input terminals.
The circuit now forms a voltage divider: V_input = V_source × (Z_in / (R_known + Z_in)). Rearranging to solve for the unknown input impedance gives you Z_in = R_known × V_input / (V_source − V_input). Choose R_known to be roughly the same order of magnitude as the impedance you expect. If it’s too small or too large relative to the actual input impedance, the voltage drop across it will be hard to measure accurately.
Op-Amp Circuit Configurations
Operational amplifier circuits have well-defined input impedance rules that depend on the feedback topology.
A noninverting amplifier has ideally infinite input impedance. The signal connects directly to the op-amp’s noninverting input, which draws essentially zero current. In practice, the input impedance is limited by the op-amp’s own specs (often hundreds of megaohms to teraohms for FET-input devices), but for most design purposes you can treat it as infinite.
An inverting amplifier is different. The input signal feeds through a resistor (commonly labeled R_i) to the inverting input, which sits at virtual ground due to negative feedback. Since one end of R_i sees the signal voltage and the other end sees approximately 0V, all the signal current flows through R_i. The input impedance equals R_i, period. This is one of the most important practical consequences of the inverting topology: your source must be able to drive a load equal to R_i.
For inverting summing amplifiers, each input channel sees only its own input resistor. Channel 1 has an input impedance of R_i1, channel 2 has R_i2, and so on. The channels don’t interact because the summing junction sits at virtual ground. Circuits that use the inverting input with feedback directly to the input node (like current-to-voltage converters) present an input impedance near zero ohms, since the feedback holds the input node at virtual ground.
Transistor Amplifier Stages
For a common-emitter BJT amplifier, the input impedance depends on the transistor’s current gain (β), its internal base-emitter resistance, and the biasing resistors. The transistor’s own input resistance, looking into the base, is approximately β × r_BE, where r_BE is the small-signal resistance of the base-emitter junction. At a collector current of 1 mA with β = 100, this works out to roughly 2,500Ω.
The total input impedance of the amplifier stage is this transistor input resistance in parallel with the biasing resistors R_1 and R_2: 1/R_in = 1/R_1 + 1/R_2 + 1/(β × r_BE). The biasing resistors often dominate and pull the input impedance lower than the transistor alone would provide. This is why many designs use bootstrapping or FET input stages when high input impedance is critical.
Transmission Line Input Impedance
When a signal travels along a transmission line (coaxial cable, microstrip, waveguide), the input impedance depends on the line’s characteristic impedance (Z_0), the load impedance at the far end (Z_L), and the electrical length of the line. For a lossless line, the formula is:
Z_in = Z_0 × [(Z_L + jZ_0 tan(βl)) / (Z_0 + jZ_L tan(βl))]
Here, β is the propagation constant (2π/wavelength) and l is the physical length of the line. The product βl, called the electrical length, is measured in radians. This equation produces some useful special cases. When the line is exactly a half-wavelength long (βl = π), the input impedance equals the load impedance regardless of Z_0. When the line is a quarter-wavelength long, Z_in = Z_0² / Z_L, which is the basis for quarter-wave impedance matching transformers. And when the load equals the characteristic impedance (Z_L = Z_0), the input impedance is simply Z_0 at any length, because there are no reflections.
Why Input Impedance Matters: Impedance Matching
The reason you calculate input impedance in the first place is usually to ensure proper signal transfer between a source and a load. Maximum power transfer occurs when the load impedance is the complex conjugate of the source impedance. That means the resistive parts must be equal, and any reactive parts must be equal in magnitude but opposite in sign (inductive reactance cancels capacitive reactance and vice versa). When no reactive components are involved, this simplifies to: load resistance equals source resistance.
In RF and transmission line work, impedance matching prevents signal reflections that cause power loss and distortion. In audio and instrumentation, the goal is usually voltage transfer rather than power transfer, which calls for a different strategy: make the input impedance much higher than the source impedance so the signal voltage isn’t divided down.
Common Input Impedance Values in Practice
Knowing typical values helps you sanity-check your calculations and choose components appropriately.
- Oscilloscopes: 1MΩ in parallel with 10 to 20 pF of capacitance. This is high enough to avoid loading most circuits at low frequencies, but the parallel capacitance becomes significant above a few megahertz.
- Microphone preamps: Typically 1.5kΩ to 3kΩ, designed to be roughly 10 times the output impedance of professional microphones (150 to 200Ω).
- Line-level audio inputs: At least 10kΩ, often much higher. Output impedances on the source side are typically 150Ω or below.
- Guitar and instrument inputs: 470kΩ minimum, with many exceeding 1MΩ. Guitar pickups have high output impedance, so the preamp input must be even higher to preserve tone and signal level.
- Hi-fi equipment with RCA connectors: Uses voltage matching with very low output impedance and high input impedance, though rarely above 100kΩ.
The general principle across all these applications is the same. When you want to transfer voltage efficiently, the input impedance of the receiving device should be many times higher than the output impedance of the source. The ratio of at least 10:1 (input to output) is a common rule of thumb that keeps signal loss below about 10%.