AIM
Design and implement a common emitter amplifier capable of amplifying a tap sound recorded using a microphone sensor.
INTRODUCTION
Audio amplification is a fundamental concept in electronics and signal processing, which is essential for enhancing and amplifying weak audio signals for speakers or other output devices. Many applications use audio amplifiers, ranging from communication devices to large sound systems.
The common emitter amplifier configuration is one of the most widely used transistor configuration in transistor-based analog circuit design. This configuration is more popular than other BJT configurations because of its significant voltage gain, ease of implementation, and versatility. It amplifies the input signals with the added phase shift of 180 degrees between input and output through a bipolar junction transistor (BJT).
In this design, a BC549 transistor was selected because of its low noise characteristics and high current gain, making it an ideal choice for audio applications. The goal of this design experiment was to design and implement a single-stage common emitter audio amplifier capable of achieving a desired voltage gain. This amplifier was designed to process audio signals effectively in the practical application by using transistor theory and circuit design principles.
The common emitter amplifier is a configuration in a BC549 transistor which is used to apply an input signal to the base-emitter junction, with an amplified output signal taken from the collector terminal. The transistor works as a current-controlled device, where a small base current $(I_B)$ controls a much larger collector current $(I_C)$ , and the result is an amplification. The relationship between these currents is defined as the transistor's DC current gain ( $\beta$ ). A transistor's Beta value, sometimes referred to as $h_{FE}$ on datasheets.
$$ \beta = \frac{I_c}{I_B} $$
The operating region of the transistor is important for amplification. In the active region of the transistor's $I_c$ - $V_{CE}$ characteristics curve, the transistor has linear behaviour, allowing the output signal is an exact reproduction of the input signal but only amplified.
Biasing is very important in amplifier design as it establishes the correct operating point of the transistor amplifier ready to receive signals, and it is reducing any distortion in the output signal.
The use of a DC load line drawn onto the output characteristics curves of an amplifier allows us to see all the possible operating points of the transistor from fully "ON" to fully "OFF", and to which the Quiescent operating point or Q-point of the amplifier can be found.
Coupling Capacitors are used to block DC components while allowing AC signals to pass. Bypass Capacitors are used to improve voltage gain by bypassing the emitter resistor for AC signals.
Resistors were used to establish biasing and stabilize the operating point.
CALCULATIONS
Given Data:
- $\beta = 150$
- $V_{BE} = 0.7V$ [from Datasheet related to BC549]
Assumptions:
- $I_c = 10mA$
- $V_{CC} = 15V$
Max $I_{C}$ is 100mA for this selected transistor (BC549).
Let's $I_c = 10mA$
$$ \begin{align*} I_{C}&=\beta I_{B} \\ I_{B}&=\frac{I_c}{\beta} \\ &=\frac{10 \times 10^{-3}}{150} \\ &=66.667 \mu A \end{align*} $$
Let's assume voltage drop across $R_E$ is equal to $10 \%$ of $V_{CC}$.
$$ \begin{align*} V_{R_E} &= 0.1V_{CC}\\ &= 0.1 \times 15 V \\ & = 1.5 V \end{align*} $$
$$ \begin{align*} I_E &= I_C + I_B \\ &= 10 mA + 66.667 \mu A \\ &= 10.066 mA \\ &\approx 10 mA \\ &\approx I_C \end{align*} $$
By using Ohms Law,
$$ \begin{align*} V_{R_E} &= I_{R_E} \times R_E \\ R_{E} &= \frac{V_{R_{E}}}{I_{R_{E}}} \\ &=\frac{1.5 V}{10 \times 10^{-3} A} \\ &= 150 \Omega \end{align*} $$
Voltage Drop at $R_{E}= 1.5 V$. Also Maximum Collector-Emitter Saturation Voltage $V_{CE(sat)}$ of this transitor is 250mV. Let's assume Collector-Emitter Saturation Voltage at the moment using the transitor is 200mV. Therefore remaining voltage from the $V_{CC}$ is should be equal to $V_C$ . But for maximum symmectrical output, $V_C$ should be half of the $V_{CC}$ .
$$ \begin{align*} 2V_{C} &= V_{CC} - V_{R_E} - V_{CE(sat)} \\ &= 15V - 1.5V - 0.2V \\ &= 13.3 V \end{align*} $$
By using Ohms law,
$$ \begin{align*} V_{R_C} &= I_{R_C} \times R_{C} \\ R_{C} &= \frac{V_{R_C}}{I_{R_C}} \\ &= \frac{\frac{1}{2} \times 13.3 \text{ V}}{10 \times 10^{-3} \text{ A}} \\ &= 665 \Omega \end{align*} $$
Base Voltage;
$$ \begin{align*} V_{BE} &= V_B - V_E \\ 0.7V &= V_B - 1.5V \\ V_B &= 0.7V + 1.5V \\ &= 2.2V \end{align*} $$
Calculating $R_1$ & $R_2$
Since the $I_B$ is much smaller current than the current that flows through $R_1$ & $R_2$ , let's assume that current is equal to 10 times of $I_B$.
$$ \begin{align*} I_{R_2} &= 10 \times I_B \\ &= 10 \times 66.667 \mu A \\ &= 666.67 \mu A \end{align*} $$
By using Ohms Law;
$$ \begin{align*} V_{R_2} &= I_{R_2} \times R_2 \\ R_2 &= \frac{V_{R_2}}{I_{R_2}} \\ &= \frac{2.2 V}{666.67 \times 10^{-6} A} \\ &= 3299.9835 \Omega \\ &\approx 3.3 k\Omega \end{align*} $$
Also;
$$ \begin{align*} R_1 &= \frac{V_{R_1}}{I_R} \\ &= \frac{15 V - 2.2 V}{666.67 \times 10^{-6} A}\\ &= 19199.904 \Omega \\ &\approx 19.2k \Omega \end{align*} $$
Coupling Capacitors ($C_{in}$ & $C_{out}$);
These capacitors used for block DC signal and allowing AC signals to pass. At low frequencies, if the impedance of capacitors is larger that can be affect the signal transmission. Therefore let's take $Z_{C(in)}$ is 10 times less than input impedance.
Input Impedance $R_{in}$ ;
$$ \begin{align*} \frac{1}{R_{in}} &= \frac{1}{R_1} + \frac{1}{R_2} \\ R_{in} &= \frac{R_1 \times R_2}{R_1 + R_2} \\ &= \frac{19.2k\Omega \times 3.3k\Omega}{19.2k\Omega + 3.3k\Omega} \\ &= 2.816 k\Omega \end{align*} $$
$$ \begin{align*} Z_{C_{in}} &= \frac{R_{in}}{10} \\ &= \frac{2.816 k\Omega}{10}\\ &= 281.6 \Omega \end{align*} $$
Lowest frequence that used in this design experiment is $20Hz$.
$$ \begin{align*} C_{in} &= \frac{1}{2\pi \times f_{min} \times Z_{C_{in}}}\\ &=\frac{1}{2\pi \times 20Hz \times 281.6 \Omega} \\ &=\frac{1}{35386.89965}F \\ &= 28.259 \mu F \\ &\approx 28\mu F \end{align*} $$
These capacitor value also can be used for $C_{\text{out}}$ .
Emitter Bypass Capacitor - $C_{E}$ ;
$$ \begin{align*} Z_{C_E} &= \frac{R_E}{10}\\ &=\frac{150 \Omega}{10} \\ &=15 \Omega \end{align*} $$
$$ \begin{align*} C_E &= \frac{1}{2\pi \times f_{min} \times Z_{C_E}} \\ &=\frac{1}{2\pi \times 20 Hz \times 15 \Omega} \\ &=\frac{1}{1884.955592} F \\ &= 530.5164 \mu F \\ &\approx 530 \mu F \end{align*} $$
Also, Input Impedance,
$$ \begin{align*} R_{in} &= \frac{V_{in}}{I_{in}}\\ &=\frac{(I_B + I_C) \times r_E}{I_B}\\ &=\frac{(I_B + \beta I_B) \times r_E}{I_B}\\ &=(1 + \beta)r_E \\ R_{BE} &= (1 + \beta)r_E \end{align*} $$
Calculating Voltage Gain - $A_v$ ;
$$ \begin{align*} V_{out} &= I_C \times R_C \\ &= -\beta I_B \times R_C \\ &= -\beta \times R_C \frac{V_{in}}{r_{BE}} \\ \frac{V_{out}}{V_{in}} &= -\frac{\beta \times R_C}{r_{BE}} \\ &= -\frac{\beta \times R_C}{(1 + \beta)r_E} \end{align*} $$
$r_{E}$ is emitter resistance.
$$ r_{E} = \frac{kT}{qI_{E}} \approx \frac{25}{I_{E}} \text{ at } T = 290K $$
Since $\beta \gt \gt \gt 1$,
$$ \begin{align*} \frac{V_{out}}{V_{in}} &\approx -\frac{R_{C}}{r_{E}}\\ &\approx -\frac{R_c \times I_E}{25} \\ &\approx -\frac{665 \Omega \times 10 mA}{25 mV} \\ &\approx -266 \end{align*} $$
Power Dissipation;
$$ P_R = \frac{V^2}{R} $$
| $R_1$ ; | $$ \begin{align*} P_{R_1} &= \frac{12.8^2}{19.2 \times 10^3}\\ &= 8.5333 \textit{mW} \end{align*} $$ |
| $R_2$ ; | $$ \begin{align*} P_{R_2} &= \frac{2.2^2}{3.3 \times 10^3}\\ &= 1.4666 \text{mW} \end{align*} $$ |
| $R_{C}$ ; | $$ \begin{align*} P_{R_C} &= \frac{6.65^2}{665}\\ &= 66.5 mW \end{align*} $$ |
| $R_{E};$ | $$ \begin{align*} P_{R_E} &= \frac{1.5^2}{150}\\ &= 15mW \end{align*} $$ |
COMPONENT SELECTION RATIONALE
-
BC549 Transistor
The BC549 is specifically designed for low-noise applications, making it ideal for audio amplification circuits where signal clarity and minimal distortion are important. The BC547 and BC548, while similar but have slightly higher noise levels than BC549, which can degrade audio quality in sensitive applications. The BC549 has a typical current gain ( $h_{FE}$ / $\beta$ ) in the range of 110-800, ensuring sufficient amplification for the input signal. Especially for Class-A Amplifier like this design experiment, it offers current gain in the range of 110-220.
-
Coupling Capacitors (for $C_{in}$ & $C_{out}$ )
Coupling capacitors are used to block DC components of the input and output signals while allowing AC signals to pass. Ceramic Capacitors or Firm Capacitors can be used.
-
Bypass Capacitors (for $C_{E}$ )
Bypass capacitors are placed in parallel with the emitter resistor ( $R_E$ ) to bypass AC signals around the emitter resistance, thereby maximizing the voltage gain of the amplifier. Without a bypass capacitor, $R_E$ would contribute to negative feedback, reducing gain. Electrolytic Capacitors can be used.
-
Resistors
Resistors are selected with power ratings that exceed their expected power dissipation to ensure reliability. Standard resistors with 0.25W and 0.125W power ratings can be used for $R_C/R_E$ and $R_1/R_2$ .
CIRCUIT DIAGRAM
SIMULATION RESULTS
PHYSICAL CIRCUIT
| Components | Calculated Value | Used Value |
|---|---|---|
| $R_1$ | $19.2\text{ k}\Omega$ | $18\text{ k}\Omega$ |
| $R_2$ | $3.3\text{ k}\Omega$ | $3.3\text{ k}\Omega$ |
| $R_C$ | $665\Omega$ | $680\Omega$ |
| $R_E$ | $150\Omega$ | $150\Omega$ |
| $C_{in}$ & $C_{out}$ | $28\mu\text{F}$ | $22\mu\text{F}$ |
| $C_E$ | $530\mu\text{F}$ | $470\mu\text{F} \parallel 100\mu\text{F}$ |
| $570\mu\text{F}$ |
*Transistor (BC549) & $V_{\text{CC}}$ didn't Change.
OSCILLOSCOPE MEASUREMENTS AND ANALYSIS
- Used Frequency – $1kHz$
- Oscilloscope Readings:
- Input Signal:
- Output Signal:
- Oscilloscope Readings:
- Input Signal:
- Output Signal:
DISCUSSION
This design report shows the design, implementation, and analysis of a single-stage common emitter audio amplifier, using a BC549 transistor. The aim of the experiment was amplifying a weak audio signal, like a tap sound recorded by a microphone sensor, and also the analysis of the performance of the circuit. Through both simulation and physical construction of the circuit, several aspects related to amplifier design and operation were explored.
The initial design phase involved by calculating resistor values for biasing the transistor in the active region to ensure the linear amplification with minimal distortion. Theoretical calculations were performed using the datasheet values related to BC549 Transistor, and assuming a target collector current of $10 mA$ and a supply voltage ($V_{CC}$) of $15V$. The input and output capacitors were selected as coupling capacitors to block DC and allow AC signal to pass. A bypass capacitor was used to improve the gain of the amplifier.
The simulation phase, which used Proteus software, allow us an initial testing of the circuit performance. Simulation was done by using an AC signal and also using Audio input with allow us to simulate a microphone. The results showed that a tap signal could be amplified using this circuit, as well as a standard AC signal.
The values of physical component that used slightly changed from the calculated values due to standard resistor and capacitor values that available in the current market. (e.g. for $R_{1}$ used $18k \Omega$ instead of 19.2kΩ, and for CE used 570μF instead of 530μF). Despite these changes, the circuit performed as expected, demonstrating the flexibility of the design. The physical testing involved using a signal generator to provide a known input, and an oscilloscope was used to observe and measure both input and output signals. Two separate measurements were taken using input signals with various amplitudes. The output signals showed a significant increase in the amplitude as expected with the implementation of an audio amplifier. The 180° phase shift between the input and output signals, characteristic of the CE amplifier, was observed.
The oscilloscope measurements showed a clean sinusoidal output for input frequencies in the audio range (20 Hz to 20 kHz). The gain of this amplifier was calculated to be around 266 according to the calculations. Following table shows the comparison of Voltage gain between calculated, simulated results and practical results.
| Calculated Voltage Gain | Results from Simulation | Results from Physical Test |
|---|---|---|
| Frequency = $1\text{kHz}$ & Amplitude = $40\text{mV}_{\text{PP}}$ | ||
| $$ \begin{align*} A_V &= \frac{V_{out}}{V_{in}}\\ &\approx \frac{R_C}{r_E} \end{align*} $$ | $$A_V = \frac{V_{\text{out}}}{V_{\text{in}}}$$ | |
| $$A_V \approx -266$$ | $$ \begin{align*} A_V &= \frac{2.24\text{V}}{14.1\text{mV}}\\ &= 158.865\\ &\approx 159 \end{align*} $$ | $$ \begin{align*} A_V &= \frac{5.3\text{V}}{40\text{mV}}\\ &= 132.5\\ &\approx 133 \end{align*} $$ |
There was some variation between calculated and physically used values for the circuit which could have led to lower amplification levels. These differences could be from resistor tolerance, specific capacitor impedance, the limited bandwidth of the oscilloscope used, or variations in the transistor parameters.
The calculated gain (-266) seems very high for a single-stage amplifier and doesn’t quite match the simulation or physical test results. This could be due to the approximation used in the calculations or due to parameters not considered for calculation, such as transistor capacitance. As previously mentioned, the use of available component values instead of calculated values, component tolerances, and the measurement equipment bandwidth limitations, as well as neglecting parasitic capacitance, could be the differences in measured and calculated values.
The design can be tested with a microphone sensor and verify whether a tap signal could be amplified with the circuit, as was the aim of this experiment.
The experimental setup successfully showed the basic functionality of a single-stage commonemitter audio amplifier, with simulations and physical tests confirming that a low audio signal can be amplified with thecorrect biasing by using BC549 Transistor.
Source:
Prasad Madhuranga @ 2024 #DMX3304 Mini Project #OUSL #Engineering
