Common Emitter BJT Applications
Spring 2019

ECE 110

Course Notes

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Suppose you want to build a temperature control system for your room. You want a fan to turn on if the temperature exceeds 78°F and to turn off when the temperature drops below 75°F. (You use different temperature thresholds to prevent the fan from oscillating between on and off.) You plan to use the following hardware:

• TMP36 temperature sensor: to measure the room temperature as a voltage signal;
• Arduino microcontroller: to compare the signal to preset thresholds and produce an on/off voltage signal;
• DC motor: to spin the fan blades if the Arduino indicates "on".

Figure 1

Fig. 1: A temperature-controlled fan circuit that does not work. The TMP36 temperature sensor is connected directly to the Arduino, which is connected directly to the motor.

There are a couple of problems when you connect the components directly.

• The TMP36 output voltage range does not match well with Arduino input voltage range. According to the TMP36 datasheet, it operates at temperatures between -40°C and 125°C (i.e. -40°F to 257°F), and within this temperature range, it outputs a voltage between 0 and 2 V. That means that at room temperatures the TMP36 output lies between about 0.7 and 0.9 V, which leads to a significant mismatch with the Arduino input voltage range of 0 to 5 V.
• The Arduino does not output enough current to start the motor. An Arduino pin can supply a maximum current of 40 mA, but a DC motor driving fan blades draws current on the order of 1 A.

Fortunately, you can solve both problems using BJTs in the common emitter configuration. In the first case, you use a common emitter amplifier to scale up the TMP36 output so that it better matches the Arduino input range. In the second case, you let the Arduino output voltage toggle a common emitter switch that controls a large current flowing through the motor.

Figure 2

Fig. 2: A temperature-controlled fan that works. A common emitter amplifier connects the TMP36 temperature sensor to the Arduino. A common emitter switch connects the Arduino to the motor.

On the rest of this page, we analyze how a BJT can function as an amplifier and a switch.

A voltage amplifier receives a voltage signal at an input port and produces a scaled-up voltage signal at an output port.

Figure 3

Fig. 3: Common emitter amplifier circuit. This amplifier circuit is the same as the common emitter circuit, except that the input voltage source is replaced with an input port $V_{\text{in}}$. The output port $V_{\text{out}}$ is taken across the collector and emitter terminals, so $V_{\text{out}}=V_{CE}$.

The input-output characteristic of this circuit is the output $V_{\text{out}}$ plotted as a function of the input $V_{\text{in}}$. We trace the plot by varying $V_{\text{in}}$ and determining the corresponding values of $V_{\text{out}}$ following the common emitter circuit analysis.

Figure 4

Fig. 4: Amplifier input-output characteristic. $V_{\text{out}}$ is constant at $V_{CC}$ in the OFF mode, linearly decreasing in the ACTIVE mode and constant at $V_{CE,\text{sat}}$ in the SATURATED mode. The transition from OFF to ACTIVE happens at $V_{\text{in}}=V_{BE,\text{on}}$ and the transition from ACTIVE to SATURATED happens at $V_{\text{in}}=V^*_{\text{in}}$, derived as $\eqref{CEA-VIN}$ below.

Notice that in the ACTIVE mode a change in $V_{\text{in}}$ leads to a change in $V_{\text{out}}$. In the common emitter circuit, the change is typically magnified from input to output, making it an amplifier. But notice also that a change in $V_{\text{in}}$ causes $V_{\text{out}}$ to change in the opposite direction, so we call this circuit an inverting amplifier. The ratio of the change in $V_{\text{out}}$ to the change in $V_{\text{in}}$ is called the gain $G$, a negative number for an inverting amplifier. The magnitude of $G$ indicates how much the input is stretched into the output and the sign of $G$ indicates whether the stretching is in the same direction or the opposite direction. In fact, the gain is the slope of the ACTIVE mode line segment:
\begin{align}
G&= \frac{V_{CE,\text{sat}}-V_{CC}}{V^*_{\text{in}}-V_{BE,\text{on}}} \label{CEA-GA1}
\end{align}
The constant output voltages $V_{CC}$ in OFF mode and $V_{CE,\text{sat}}$ in SATURATED mode are explained by the behavior of $V_{CE}$ in those modes. The transition input voltage $V_{BE,\text{on}}$ between OFF and ACTIVE is the boundary between the conditions on $V_{\text{in}}$ in those modes.

At the transition input voltage between ACTIVE and SATURATED, the BJT obeys the behavior of both of these modes. In particular, we follow these steps to derive $V^*_{\text{in}}$:
\begin{aligned}
I_C&=I_{C,\text{sat}}=\frac{V_{CC}-V_{CE,\text{sat}}}{R_2}& &\text{SATURATED mode }I_C\text{ formula} \\
I_B&=\frac{I_C}{\beta}& &\text{from ACTIVE mode }I_C\text{ formula} \\
V^*_{\text{in}}&=V_{\text{in}}=V_{BE,\text{on}}+I_B R_1& &\text{from ACTIVE mode }I_B\text{ formula}
\end{aligned}
The overall expression is:
\begin{align}
V^*_{\text{in}}&= V_{BE,\text{on}}+\frac{R_1}{\beta R_2}(V_{CC}-V_{CE,\text{sat}}), \label{CEA-VIN}
\end{align}
where $V_{CC}$, $R_1$ and $R_2$ are known circuit constants and $\beta$, $V_{BE,\text{on}}$ and $V_{CE,\text{sat}}$ are known BJT parameters. Substituting equation $\eqref{CEA-VIN}$ into equation $\eqref{CEA-GA1}$, gives another formula for the gain of the common emitter amplifier:
\begin{align}
G&= -\frac{\beta R_2}{R_1} \label{CEA-GA2}
\end{align}
We now see what happens when $V_{\text{in}}$ is a voltage waveform.

Figure 5

Fig. 5: Voltage signal amplification. If $V_{\text{in}}$ is a signal between $V_{BE,\text{on}}$ and $V^*_{\text{in}}$, then $V_{\text{out}}$ is an amplified and inverted copy that exists between $V_{CC}$ and $V_{CE,\text{sat}}$.

Figure 6

Fig. 6: Voltage signal amplification with clipping. If $V_{\text{in}}$ is a signal that goes below $V_{BE,\text{on}}$ and above $V^*_{\text{in}}$, then $V_{\text{out}}$ is an amplified and inverted copy that is clipped at $V_{CC}$ above and $V_{CE,\text{sat}}$ below.

A common emitter switch for an actuator (such as a DC motor) receives a voltage signal at an input port and controls an output current through the actuator.

Figure 7

Fig. 7: Common emitter switch circuit. This switch circuit is the same as the common emitter circuit, except that the resistor $R_2$ is replaced by a DC motor (with modeled internal resistance $R_2$) and the input voltage source is replaced with an input voltage port $V_{\text{in}}$. The output current $I_{\text{out}}$ flows through the motor into the collector, so $I_{\text{out}}=I_C$. Since the internal resistance of the motor is $R_2$, the common emitter formulas apply to this circuit too.

Because the output is a current, the input-output characteristic is $I_{\text{out}}$ as a function of $V_{\text{in}}$. Similar to the case of the common emitter amplifier, we trace the plot by varying $V_{\text{in}}$ and determining the corresponding values of $I_{\text{out}}$ following the common emitter circuit analysis.

Figure 8

Fig. 8: Switch input-output characteristic. $I_{\text{out}}$ is zero in the OFF mode, linearly increasing in the ACTIVE mode and constant at $I_{C,\text{sat}}$ in the SATURATED mode. The transition from OFF to ACTIVE happens at $V_{\text{in}}=V_{BE,\text{on}}$ and the transition from ACTIVE to SATURATED happens at $V_{\text{in}}=V^*_{\text{in}}$, derived as $\eqref{CEA-VIN}$ above. Note that the vertical axis is $I_{\text{out}}$, unlike in Fig. 4.

Notice that if $V_{\text{in}}$ toggles between values $V_{\text{in}} < V_{BE,\text{on}}$ and $V_{\text{in}} > V^*_{\text{in}}$, then the BJT toggles between the OFF and SATURATED modes, and $I_{\text{out}}$ toggles between 0 and $I_{C,\text{sat}}$, respectively. As long as $I_{C,\text{sat}}$ is designed to be large enough to start the motor, the input voltage signal (itself supported by a small current) can switch the motor on and off.

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