26. BJT Common Emitter Amplifier

26.1. Objective

The purpose of this experiment is to investigate the common emitter configuration using the BJT device.

26.2. Notes

In this tutorials we use the terminology taken from the user manual when referring to the connections to the Red Pitaya STEMlab board hardware.

Oscilloscope & Signal generator application is used for generating and observing signals on the circuit.

Extension connector pins used for +5 V, -3.3 V and +3.3 V voltage supply are show in the documentation here.

26.3. Background

The configuration, shown in Fig. 1, demonstrates an npn transistor used as a common-emitter amplifier. Output load resistor \(R_L\) is chosen such that for the desired nominal collector current \(I_C\), approximately one third of the +5 V voltage (1.6 V) appears at \(V_{CE}\) (at DC operating point condition). Resistor \(R_B\) sets the nominal bias operating point for the transistor (base current \(I_B\)) to sink the required collector current \(I_C\). The input signal is AC coupled to the base of the transistor with capacitor \(C_1\) to not disturb DC bias conditions. Voltage divider \(\frac{R_1}{R_2}\) is chosen to provide a self-biased DC operating point. Resistor \(R_E\) is used to add emitter degeneration (current feedback) in order to stabilize the DC operating point.

The best approach for selecting the \(R_L\) and \(R_E\) is to enable voltage drops across \(Q_1\), \(R_L\) and \(R_E\) equal to the 1/3 of the \(V_{CC}\) (at DC operating point condition). Therefore \(R_E\) = \(R_L\). Adding the emitter degeneration resistor has improved the stability of the DC operating point at the cost of reduced amplifier gain. A higher gain for AC signals can be restored to some extent by adding capacitor \(C_E\) across the degeneration resistor \(R_E\), effectively setting the ” \(R_E\) ” value close to zero for AC signals. Capacitor \(C_2\) is added to block the DC component of the output signal.

Note

How to design an common-emitter amplifier is nicely explained in a video tutorial on The Signal Path Youtube channel.

_images/Activity_26_Fig_01.png

Figure 1: Common-emitter amplifier configuration

26.4. Quick calculation of the common emitter amplifier

Suppose that we want to design an amplifier with the gain \(A = 5\) using npn transistor 2N3904 and a voltage supply of \(V_{CC} = 5V\).

For the npn transistor 2N3904 we can assume that \(\beta = 100\) and \(v_{CE_{sat}} = 0.2 V\). First step is to set DC operating point by deciding voltages across \(R_L\), \(R_E\) and \(Q_1\).

\[V_{R_L}+(V_{CE}+v_{CE_{sat}})+V_{R_E} = V_{CC} \quad (1)\]

If we take into account \(v_{CE_{sat}}\) and 1/3 ratio of voltages on \(R_L\), \(R_E\) and \(Q_1\) we get following:

\[1.6 V + 1.6 V + 0.2 V + 1.6 V = 5 V \quad (2)\]

From desired value of gain \(A\) we can calculate \(R_L\) using Eqs. (3) – (7)

\[A = \beta \frac{R_{out}}{R_{in}}. \quad (3)\]

where \(R_{out}\) is the resistor connected in series with the collector and \(R_{in}\) is the resistor connected in series with the base.

\[R_{out} = R_L \quad \text{and,} \quad R_{in} = R_{B} \quad (4)\]

It follows:

\[A = \beta \frac{R_L}{R_B} \quad (5)\]

In this step we need to set current ratings of our amplifier i.e we need to choose \(I_C\) to calculate \(R_L\).

Let’s set \(I_C = 5 mA\), then

\[R_L = \frac{V_{R_L}}{I_C} = \frac{1.6V}{5mA} = 320 \Omega \quad (6)\]

In order to satisfy Eq. (2) it follows that:

\[R_E = R_L, \quad \text{i.e.} \quad R_E = \frac{V_{R_L}}{I_C} = 320 \Omega. \quad (7)\]

Now we can calculate \(R_{in}\) i.e \(R_{B}\) value as:

\[R_{B} = \beta \frac{R_L}{A} = 100 \frac{320 \Omega }{5} = 6.4k \Omega. \quad (8)\]

The last step is to calculate values of DC bias resistors \(R_1\) and \(R_2\). \(R_2\) can be obtained from “cookbook” relation given in Eq. (9) and therefore \(R_1\) can be calculated from Eq. (10).

\[ \begin{align}\begin{aligned}R_2 &\approx 10 R_E \quad (9)\\R_2 &= 3.2 k \Omega\end{aligned}\end{align} \]
\[R_1 = \frac{V_{CC} - (v_{BE}+V_{R_E})}{\frac{(v_{BE}+V_{R_E})}{R_2}} \quad (10)\]

where \(v_{BE} = 0.6 V\)

\[R_1 = \frac{5V - (0.6V+1.6V)}{ \frac{(0.6V + 1.6V)}{3.2k \Omega}} = 4.0k \Omega\]

Note

Above shown calculation of the common emitter amplifier should be use as a guideline and not as a definitive design blueprint. The reason for this is that in majority of cases calculated values of the resistors will be outside of the resistors values available on the market. Therefore resistor values should be rounded or changed in order to fit them to the closes values of commonly available resistors. It is a good practice to set \(R_1\) and \(R_B\) as potentiometer since with this two resistors we can manually tune the amplifier. Tuning the amplifier is necessary since transistors can differ from each other.

Selecting the values of capacitors \(C_1\), \(C_2\) and \(C_E\) is done by using high value capacitors while the maximum voltage rating of the capacitors must be larger than \(V_{CC}\). Commonly an electrolytic capacitors are used in ranges of \(\mu F\). If we want to bring (emitter - gnd) impedance (for AC) close to zero then \(C_E\) must be large as possible. Also \(C_1\) , \(C_2\) should be large to prevent large voltage drops across them.

26.5. Materials

  • Red Pitaya STEMlab
  • 2x 470Ω Resistor
  • 2x 10kΩ Resistor
  • 1x 10kΩ Trimer
  • 1x 1kΩ Resistor
  • 1x 10uF Capacitor
  • 2x 4.7uF Capacitor
  • 1x small signal npn transistor (2N3904)
  • 1x Solder-less Breadboard

26.6. Procedure

Following calculations and guidelines above we have built common emitter amplifier shown in figure 2. We had an \(470 \Omega\) resistors available and those resistors where used for \(R_L\) and \(R_E\). After selecting the \(R_L\) and \(R_E\) the other components have been calculated and selected.

_images/Activity_26_Fig_02.png

Figure 2: Common emitter amplifier with components values

  1. Build the circuit on from figure 2 on the breadboard.
_images/Activity_26_Fig_03.png

Figure 3: Common emitter amplifier on the breadboard

  1. Start the Oscilloscope & Signal generator application
  2. In the OUT1 settings menu set Amplitude value to 0.1V, DC offset to 0 V and frequency to 10kHz to apply the input voltage. From the waveform menu select SINE, deselect SHOW button and select enable.
  3. On the left bottom of the screen be sure that IN1 and IN2 V/div are set to 200mV/div (You can set V/div by selecting the desired channel and using vertical +/- controls)
  4. Set t/div value to 20us/div (You can set t/div using horizontal +/- controls)
  5. In the trigger menu settings and select NORMAL
  6. In the measurements menu select P2P for IN1 and IN2
_images/Activity_26_Fig_04.png

Figure 4: Common emitter amplifier measurements

On figure 3 the measurements of the common emitter amplifier is shown. From the P2P measurements we can calculate achieved gain and it is approximately \(A \approx 9\).

26.7. Questions

  1. Try to change value of \(R_{B_{pot}}\) and observe the change in the gain?
  2. What is the maximum voltage swing of the output signal?
  3. Increase OUT1 frequency and try to measure amplifier bandwidth.

For question 2 follow next:

Set the IN2 scope probe to x10, in the IN2 menu set probe attenuation to 10 and increase OUT1 amplitude to 0.2V. What is the P2P value of the IN2?

With gain \(A = 9\), input signal P2P amplitude 0.4V the output P2P(IN2) value should be \(0.4 \times 9 = 3.6 V\) ! But it is not? Signal is cut off! Can you explain why?

Hint

Check the calculations above and voltages across \(V_{CE}\)