Voltage reference

A voltage reference is a circuit that produces a stable, known voltage that barely moves when the supply voltage or the load changes. The two simple diode-based references in this course are a string of forward-biased diodes (each contributing its near-constant ~0.7 V drop) and a Zener diode in breakdown. Both work because the diode’s voltage is almost insensitive to current, so its small slope-resistance (Diode small-signal resistance $r_d$, or Zener dynamic resistance $r_z$) makes the output stiff against disturbances.

The forward-diode reference: why it is stable

Stack $n$ forward-biased diodes in series and feed them through a resistor from the supply. Each diode drops ~0.7 V, so the reference is $\approx 0.7n$ V. Three diodes give about 2.1 V. The reference is stable because each diode’s voltage changes only $r_d$ per unit current, and $r_d=V_T/I_D$ is tiny. When the supply wobbles, almost the whole wobble falls across the series resistor, not across the diodes.

Worked example: three-diode 2.1 V reference

Three diodes in series, $V_{DD}=10\text{V}\pm 1\text{V}$, series resistor $R=1$ k$\Omega$. The three diodes drop $3\times 0.7=2.1$ V.

Bias current. By KVL the current is set by what is left after the diode stack:

$I_D=\frac{V_{DD}-3V_D}{R}=\frac{10-2.1}{1\text{k}\Omega }=7.9\text{mA}$

Each diode’s small-signal resistance:

$r_d=\frac{V_T}{I_D}=\frac{25\text{mV}}{7.9\text{mA}}\approx 3.2\Omega$

Three in series present $3\times 3.2=9.6\Omega$ to a change at the supply.

Effect of the ±1 V supply variation. The reference and the series resistor form a divider for the change. A 1 V change at the supply produces a change in the reference of

$\Delta V_d\approx \Delta V_{DD}\cdot \frac{3r_d}{3r_d+R}=1\text{V}\cdot \frac{9.6}{9.6+1000}\approx 9.5\text{mV}$

That is about $9.5\text{mV}/2.1\text{V}\approx 0.45\%$. So a $\pm 10\%$ swing on the 10 V supply moves the 2.1 V reference by less than half a percent — the string of diodes has regulated the voltage. The smaller $r_d$ is (i.e. the higher the bias current, up to power limits), the stiffer the reference.

Three series diodes as a 2.1 V reference; small $r_d$ makes it insensitive to supply variation.

A Zener voltage regulator does the same job with one device instead of a stack and at an arbitrary $V_Z$ rather than a multiple of 0.7 V; the math is identical with $r_z$ in place of $3r_d$. Either way the principle is: a low slope-resistance turns a current-disturbance into a negligible voltage-disturbance.