Unijunction Transistor (UJT)

1. Theory

• Definition: A unijunction transistor (UJT) is a three-terminal switching device made of a lightly doped N-type silicon bar with ohmic contacts at both ends and a single PN emitter junction part-way along it.
• No transistor action: Despite its name, there is no amplification or regenerative PNPN loop; it is not part of the thyristor family.
• Terminals: Base 1 ($B_1$), base 2 ($B_2$) at the two ends of the bar, and the P-type emitter (E).
• Resistive divider: The bar splits into $R_{B1}$ and $R_{B2}$, so the bar potential at the emitter is $\eta V_{BB}$, where $\eta =R_{B1}/R_{BB}$ (typically 0.5 to 0.8).
• Conductivity modulation: Holes injected by the emitter raise the conductivity of the $B_1$ section and lower $R_{B1}$, the same effect as in a PIN diode.

2. Working Principle

• Off state: While the emitter voltage is below $\eta V_{BB}+V_D$, the emitter junction is reverse biased and only leakage flows.
• Peak point: At $V_P=\eta V_{BB}+V_D$ the emitter junction turns on and starts injecting holes into the $B_1$ region.
• Negative resistance: Falling $R_{B1}$ pulls the divider voltage down, forward-biasing the emitter harder, so emitter voltage falls as emitter current rises.
• Valley point: Beyond the valley current, the $B_1$ region is saturated with carriers and the characteristic turns positive again.
• Relaxation oscillation: A capacitor charges through $R_E$ to $V_P$ and discharges through the emitter; the period $T\approx R_{E}C\ln \left[1/(1-\eta )\right]$ is nearly independent of supply voltage.
• Load-line window: $R_E$ must lie between the valley and peak limits for oscillation to continue.

3. Applications

• Current status: Largely obsolete; 555 timers, microcontrollers and dedicated gate-driver ICs have replaced it.
• Historical role: Relaxation oscillators, sawtooth generators, timing circuits and SCR/TRIAC trigger-pulse generators.

Name	Formula	Related Formulae	Variables/Constants
Interbase resistance	$R_{BB}=R_{B1}+R_{B2}=\frac{L}{q{\mu }_n{N}_{D}A}$	$I_{B2}=\frac{V_{BB}}{R_{BB}}(I_E=0)$	$\begin{array}{r}{R}_{BB}:totalbarresistancebetween{B}_1\\ and{B}_{2}withtheemitteropen\end{array}$ $\begin{array}{r}{R}_{B1},R_{B2}:barresistancebelowand\\ abovetheemitterjunction\end{array}$ $L,A:barlengthandcross-sectionalarea$ $N_D:n-typedoping$ $V_{BB}:interbasesupplyvoltage$
Intrinsic standoff ratio	$\eta =\frac{R_{B1}}{R_{B1}+R_{B2}}=\frac{R_{B1}}{R_{BB}}$	$\eta \approx \frac{x_E}{L}$	$\begin{array}{r}\eta :intrinsicstandoffratio(typically\\ about0.5\text{–}0.8)\end{array}$ $\begin{array}{r}{x}_E:distancefrom{B}_{1}totheemitter\\ junction(uniformbarapproximation)\end{array}$
Divider voltage at the emitter junction	$V_A=\eta V_{BB}$		$\begin{array}{r}{V}_A:potentialofthen-typebar\\ attheemitterjunction(emitteropenor\\ reversebiased)\end{array}$
Peak-point (firing) voltage	$V_P=\eta V_{BB}+V_D$	$V_D\approx 0.5\text{–}0.7\mathrm{V}\text{(see PN Junction Diode page)}$	$\begin{array}{r}{V}_P:emittervoltageatwhichthe\\ junctionbecomesforwardbiasedand\\ injectionbegins\end{array}$ $\begin{array}{r}{V}_D:forwardturn-onvoltageof\\ theemitterjunction\end{array}$
Conductivity modulation	$\sigma =q\left[{\mu }_n{N}_D+({\mu }_n+{\mu }_p)\Delta p\right]$	$R_{B1}(I_E)\downarrow \text{as}\Delta p\propto I_E\text{increases}$	$\sigma :conductivityofthe{B}_{1}sectionofthebar$ $\Delta p:injectedholeconcentration$ ${\mu }_n,{\mu }_p:electronandholemobilities$
Negative-resistance region	$\frac{d{V}_E}{d{I}_E}<0(I_P<I_E<I_V)$	$V_V<V_P,I_V>I_P$	$(V_P,I_P):peakpoint$ $(V_V,I_V):valleypoint$ $\begin{array}{r}\text{(falling}{R}_{B1}\text{pulls}\text{the}\text{divider}\\ \text{voltage}{V}_A\text{down}\text{faster}\text{than}{I}_E\text{raises}\\ V_E\text{)}\end{array}$
Relaxation oscillator period	$T=R_{E}C\ln \left(\frac{V_{BB}-V_V}{V_{BB}-V_P}\right)\approx R_{E}C\ln \left(\frac{1}{1-\eta }\right)$	$f=\frac{1}{T}$	$T:oscillationperiod$ $\begin{array}{r}{R}_E,C:timingresistorandcapacitoron\\ theemitter\end{array}$ $\begin{array}{r}\text{(approximation}\text{assumes}{V}_V\ll V_{BB}\\ \text{and}{V}_D\ll \eta V_{BB}\text{)}\end{array}$
Oscillation condition on the emitter resistor	$\frac{V_{BB}-V_V}{I_V}<R_E<\frac{V_{BB}-V_P}{I_P}$	$\begin{array}{r}\text{(load}\text{line}\text{must}\text{cross}\text{the}\\ \text{negative-resistance}\text{region)}\end{array}$	$\begin{array}{r}\text{(too}\text{large}\text{an}{R}_E\text{cannot}\text{supply}{I}_P\text{to}\\ \text{fire}\text{the}\text{UJT;}\text{too}\text{small}\text{an}{R}_E\text{supplies}\\ \text{more}\text{than}{I}_V\text{and}\text{the}\text{UJT}\text{stays}\text{on)}\end{array}$

Important Questions

Ques: How does a UJT actually switch on, and where does its negative resistance come from?

With the emitter open, the bar acts as a resistive divider, so the bar potential at the emitter junction is $V_A=\eta V_{BB}$. While $V_E$ is below $V_A+V_D$, the emitter junction is reverse or only weakly biased and only a small leakage current flows. When $V_E$ reaches the peak-point voltage $V_P=\eta V_{BB}+V_D$ the junction turns on and injects holes into the $B_1$ section of the bar. These holes (with matching extra electrons) raise the conductivity there, $\sigma =q[{\mu }_n{N}_D+({\mu }_n+{\mu }_p)\Delta p]$, so $R_{B1}$ falls, which lowers the divider voltage $V_A$ and forward biases the emitter even harder, drawing more current. The emitter voltage therefore falls while the emitter current rises, which is the negative-resistance region between the peak point and the valley point. This is conductivity modulation like the PIN diode’s, but triggered by a voltage threshold set by the bar divider rather than by a regenerative PNPN loop. Reference: J. Millman and C.C. Halkias, Integrated Electronics, McGraw-Hill, 1972; General Electric Transistor Manual, 7th ed., 1964.

Ques: Why is the oscillation period set almost entirely by $R_E$, $C$ and $\eta$?

Charging the emitter capacitor toward $V_{BB}$ through $R_E$ takes the time $T=R_{E}C\ln \left[\frac{V_{BB}-V_V}{V_{BB}-V_P}\right]$ to go from the valley voltage to the peak voltage. Because $V_P\approx \eta V_{BB}$ scales with the supply, $V_{BB}$ cancels from the ratio and the period becomes $R_{E}C\ln [1/(1-\eta )]$ under the stated approximations. The ratio $\eta$ is set by the geometry of the bar (roughly the emitter position divided by the bar length), and since temperature changes $R_{B1}$ and $R_{B2}$ nearly in proportion, $\eta$ drifts only slightly even though the absolute resistance $R_{BB}$ changes. The result is a simple relaxation oscillator whose frequency is stable against supply variation, which is why UJTs were widely used as timing and SCR/TRIAC trigger circuits. Reference: J. Millman and C.C. Halkias, Integrated Electronics, McGraw-Hill, 1972.

Ques: Why must $R_E$ lie within a specific window for the circuit to oscillate?

The emitter circuit forms a load line $V_E=V_{BB}-I_E{R}_E$ that must intersect the UJT’s characteristic in the negative-resistance region for relaxation oscillation. If $R_E$ is too large, the supply cannot deliver the peak current $I_P$ at $V_P$, so the UJT never fires. If $R_E$ is too small, the circuit supplies more than the valley current $I_V$ continuously, so the device latches in its on-state and never relaxes back to the off-state. The inequality $\frac{V_{BB}-V_V}{I_V}<R_E<\frac{V_{BB}-V_P}{I_P}$ expresses exactly these two requirements, and it is the UJT-specific design constraint to check against the datasheet values of $I_P$ and $I_V$. Reference: J. Millman and C.C. Halkias, Integrated Electronics, McGraw-Hill, 1972.

Related pages in this vault: Programmable Unijunction Transistor (PUT), Thyristor (SCR), Triode for Alternating Current (TRIAC), Diode for Alternating Current (DIAC), Gate Turn Off (GTO), PN Junction, Insulated Gate Bipolar Transistor (IGBT), Tunnel or Esaki Diode, Photodetectors (PIN and Avalanche Photodiodes).