BJT Biasing

Semiconductor Devices · BJT · Learn

Why bias? A BJT amplifier is just a transistor in active mode with a DC operating point — the Q-point. Sit too close to cutoff and the output clips on the bottom; too close to saturation and it clips on the top. The job of a bias network is to plant the Q-point in the middle of the active region and keep it there as $\beta$ , temperature, and part-to-part variation try to drag it around.

Figure 1. The Q-point sits on the load line, between cutoff and saturation. A mid-load-line Q-point gives equal headroom for output swing.

The load line

Figure 2. The DC load line is the locus of all (

V_{CE}

I_C

) the circuit can reach. Endpoints come straight from KVL:

V_{CC}

on the x-axis and

V_{CC} / (R_C + R_E)

on the y-axis.

KVL around the output loop: $V_{CC} = I_C \cdot R_C + V_{CE} + I_E \cdot R_E$ . Since $I_E \approx I_C$ for sensible $\beta$ , this is a straight line in the $(V_{CE}, I_C)$ plane.
Right endpoint: $I_C = 0 \Rightarrow V_{CE} = V_{CC}$ — transistor in cutoff, all of $V_{CC}$ dropped across it.
Left endpoint: $V_{CE} = 0 \Rightarrow I_C = V_{CC} / (R_C + R_E)$ — transistor in saturation, full current limited by the resistors only.

The Q-point is the intersection of the load line (set by the output loop and

V_{CC}

) with the bias line (the

I_C

the input network commands).

Fixed bias — simple but unstable

Figure 3. Fixed bias drives

I_B

directly through

R_B

I_C = \beta \cdot I_B

tracks

\beta

1-for-1 — the Q-point shifts wildly across parts and temperature.

Fixed bias: a single resistor $R_B$ from $V_{CC}$ to the base. $I_B = (V_{CC} - V_{BE}) / R_B$ .
$I_C = \beta \cdot I_B$ . If $\beta$ doubles, so does $I_C$ . The Q-point is at the mercy of $\beta$ .
Fine for ON/OFF switching where you just need to overdrive into saturation. Useless for linear amplification where the Q-point must stay put.

Voltage-divider bias — stiff and stable

Figure 4. Voltage-divider bias.

R_1

and

R_2

set a stiff

V_B

;

R_E

turns any change in

I_C

into a change in

V_{BE}

that pushes back.

The Thevenin form simplifies the analysis:

V_{TH} = V_{CC} \cdot R_2 / (R_1 + R_2),\quad R_{TH} = R_1 \| R_2

I_E = (V_{TH} - V_{BE}) / (R_E + R_{TH} / (\beta + 1))

If the divider is stiff — $R_{TH} \ll (\beta + 1) \cdot R_E$ — the second term in the denominator vanishes and $I_E \approx (V_{TH} - V_{BE}) / R_E$ . No $\beta$ in sight.
The R_E trick: if $I_C$ tries to rise (β rises, T rises, part-to-part), the emitter voltage rises with it, $V_{BE} = V_B - V_E$ drops, the diode cuts back, and $I_C$ falls back. Negative feedback.
Design rule: pick the divider current $I_{R_2} \gtrsim 10 \cdot I_B(\text{max})$ so the divider stays stiff regardless of base loading.

Emitter bias — same trick, dual rails

Figure 5. Emitter bias uses ±

V_{CC}

rails. The base sits at ground via a small

R_B

; the emitter sees

-V_{EE}

through

R_E

. Same β-independence as voltage-divider bias.

With a base near 0 V, the emitter sits at $-V_{BE} \approx -0.7\,\text{V}$ . Across $R_E$ we drop almost the full $V_{EE}$ .
$I_E \approx (V_{EE} - V_{BE}) / R_E$ . β-independent — same mechanism as voltage-divider bias.
Common in op-amp differential input stages where dual rails are already there for free.

Temperature

Figure 6.

V_{BE}

drops about 2 mV per °C as temperature rises. From 25 °C to 100 °C that's a 0.15 V shift — enough to walk a fixed-bias Q-point clean off the load line.

$V_{BE}$ has a temperature coefficient of about $-2\,\text{mV/°C}$ .
In voltage-divider bias the dominant term is $V_{TH} - V_{BE}$ . For $V_{TH}$ in the volts and a 0.15 V shift in $V_{BE}$ , the change is small.
In fixed bias the dominant term is $V_{CC} - V_{BE}$ — same ratio — but $\beta$ also rises with temperature, compounding the drift.