= Impedance bridging
{wiki}
= Voltage bridging
{synonym}
\b[Impedance bridging], also called <voltage bridging>, connects a source to a much higher <load impedance> so that little signal <electric potential difference> is lost across the source's <output impedance>. It is useful when the receiver should observe a signal while drawing little <electric current> from its source.
Represent a linear source at one <frequency> by open-circuit <phasor> $V_s$ and series <electrical impedance> $Z_s$. With receiving <input impedance> $Z_L$, the <voltage divider> gives
$$
H=\frac{V_L}{V_s}=\frac{Z_L}{Z_s+Z_L}=\frac1{1+Z_s/Z_L}.
$$
Thus $|Z_s/Z_L|\ll1$ makes $H$ close to one as a <complex number>, controlling both amplitude and phase loading. For positive <electrical resistances>, the relative voltage loss is $R_s/(R_s+R_L)$. A $1\,\mathrm{k\Omega}$ source feeding $99\,\mathrm{k\Omega}$ retains $99\%$ of its open-circuit voltage; feeding $9\,\mathrm{k\Omega}$ retains $90\%$.
For a tolerance $\eta$ on that resistive relative loss,
$$
\frac{R_s}{R_s+R_L}\le\eta
\quad\Longleftrightarrow\quad
\frac{R_L}{R_s}\ge\frac{1-\eta}{\eta}.
$$
The often convenient ten-to-one ratio is therefore a chosen accuracy compromise, not a universal definition. A one-percent limit requires at least a ninety-nine-to-one ratio in this ideal resistive model. <Voltage divider loading error> gives the related loading problem when the source is itself a divider.
<Impedance bridging with capacitive input> explains why a large DC <electrical resistance> is not enough at every <frequency>. With source resistance $R_s$ and receiving $R_{\rm in}$ in parallel with <capacitance> $C_{\rm in}$,
$$
H(\omega)=\frac1{1+R_s/R_{\rm in}+\mathrm i\omega R_sC_{\rm in}}.
$$
At $R_s=1\,\mathrm{k\Omega}$ and $R_{\rm in}=1\,\mathrm{M\Omega}$, the DC ratio is about $0.999$. With $C_{\rm in}=100\,\mathrm{pF}$, its magnitude at $1\,\mathrm{MHz}$ is only about $0.846$. The capacitive path loads the source despite the high DC input resistance.
Texas Instruments' three-amplifier presentation motivates high-input-impedance buffering by explicitly showing that source current and nonzero source <output impedance> degrade accuracy.<Instrumentation amplifier (IA) topologies: three-amp by Tamara Alani>[Presentation slides 3–5, PDF pp. 3–5]{ref} A buffer changes the load seen by the signal source; its own finite input and output behavior still matter.
<Impedance matching> has a different objective in maximum-power-transfer applications. For a resistive source, choosing equal source and load resistances gives half the open-circuit voltage, whereas bridging seeks a ratio near one. Signal fidelity, delivered power and high-frequency transmission behavior require their appropriate models.
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