AC CE Calculator (Common Emitter Amplifier)

Analyze the AC small-signal performance of a BJT Common Emitter amplifier circuit.

What is an AC CE Calculator?

An AC CE (Alternating Current Common Emitter) calculator is a tool designed for electronics engineers, students, and hobbyists to analyze the small-signal AC performance of a common-emitter amplifier. This is one of the most fundamental and widely used transistor amplifier configurations. The calculator determines key performance metrics such as voltage gain (Av), input impedance (Zin), and output impedance (Zout) based on the circuit’s component values. Understanding these parameters is crucial for designing and troubleshooting amplifier circuits used in everything from audio preamps to radio frequency applications. The primary purpose of this amplifier is to increase the magnitude of a small AC input signal. This calculator helps predict how much amplification a specific circuit design will provide.

Common Emitter Amplifier Formula and Explanation

The calculations involve a two-step process: first, a DC analysis to find the transistor’s operating point (Q-point), and second, an AC analysis using the small-signal model. The output signal of a CE amplifier is 180 degrees out of phase with the input, which is why voltage gain is negative.

Formulae Used:

1. DC Analysis:
   • Thevenin Voltage (Vth): `Vth = Vcc * (R2 / (R1 + R2))`
   • Thevenin Resistance (Rth): `Rth = (R1 * R2) / (R1 + R2)`
   • Emitter Current (IE): `IE = (Vth – Vbe) / (RE + (Rth / Beta))` (where Vbe ≈ 0.7V)
   • Collector Current (IC): `IC ≈ IE`
2. AC Analysis:
   • Internal Emitter Resistance (re’): `re’ = 26mV / IE`
   • Voltage Gain (Av): `Av = -RC / (RE + re’)` (Unbypassed) OR `Av = -RC / re’` (Bypassed)
   • Input Impedance (Zin): `Zin = R1 || R2 || (Beta * (re’ + RE))` (Unbypassed) OR `Zin = R1 || R2 || (Beta * re’)` (Bypassed)
   • Output Impedance (Zout): `Zout ≈ RC`

Variables for the AC CE Calculator

Variable	Meaning	Unit	Typical Range
Vcc	DC Power Supply Voltage	Volts (V)	5 – 30 V
Beta (hFE)	Transistor DC Current Gain	Unitless	50 – 300
R1, R2, RC, RE	Biasing and Load Resistors	Kilo-ohms (kΩ)	0.1 – 100 kΩ
re’	AC Internal Emitter Resistance	Ohms (Ω)	5 – 100 Ω
Av	AC Small-Signal Voltage Gain	Unitless (V/V)	-10 to -500

Practical Examples

Example 1: High Gain (Bypassed Emitter)

Let’s consider a standard circuit designed for high voltage gain. The emitter resistor is bypassed with a capacitor, making its impedance near zero for AC signals.

• Inputs: Vcc = 12V, Beta = 150, R1 = 22kΩ, R2 = 4.7kΩ, RC = 4.7kΩ, RE = 1kΩ, Emitter Bypassed = Yes.
• Calculation: The DC analysis yields an `IC` of about 1.15 mA. This gives a very small `re’` of approximately 22.6 Ω.
• Results: The voltage gain `Av = -RC / re’` = -4700 / 22.6 ≈ -208. The input impedance will be relatively low. This configuration provides significant amplification.

Example 2: Stable, Lower Gain (Unbypassed Emitter)

Now, let’s remove the bypass capacitor. The full emitter resistance is now part of the AC circuit, a technique known as emitter degeneration.

• Inputs: Vcc = 12V, Beta = 150, R1 = 22kΩ, R2 = 4.7kΩ, RC = 4.7kΩ, RE = 1kΩ, Emitter Bypassed = No.
• Calculation: The DC conditions and `re’` remain the same (IC ≈ 1.15 mA, re’ ≈ 22.6 Ω).
• Results: The voltage gain `Av = -RC / (RE + re’)` = -4700 / (1000 + 22.6) ≈ -4.6. The gain is much lower and more predictable, and the input impedance is significantly higher. For more info, check out this guide on understanding BJT transistors.

How to Use This AC CE Calculator

Using the calculator is straightforward. Follow these steps for an accurate analysis of your common emitter amplifier design.

1. Enter Component Values: Input your known values for the DC supply voltage (Vcc) and all resistors (R1, R2, RC, RE). Ensure you are using the correct units (Volts and Kilo-ohms).
2. Set Transistor Beta: Input the DC current gain (Beta or hFE) of your specific transistor. This can be found in its datasheet. A typical value for common NPN transistors like the 2N3904 is 100-300.
3. Set AC Input Voltage: Provide the peak AC input voltage in millivolts (mV). This is used to calculate the resulting output voltage.
4. Select Emitter Bypass Option: Check the box if your design includes a bypass capacitor across the emitter resistor RE. This has a major impact on the voltage gain calculator results and input impedance. Bypassing yields higher gain but lower stability.
5. Interpret the Results: The calculator automatically updates the Voltage Gain (Av), Input Impedance (Zin), Output Impedance (Zout), and the DC Collector Current (IC). The chart visualizes the amplification.

Key Factors That Affect AC CE Performance

Several factors can influence the real-world performance of a common-emitter amplifier. A good design must account for these variables.

• Transistor Beta (hFE): This parameter can vary significantly even between transistors of the same part number, and it also changes with temperature and collector current. A design that relies heavily on a precise Beta value will be unstable. Using an unbypassed emitter resistor helps stabilize the circuit against Beta variations.
• Temperature: The internal emitter resistance (`re’`) is dependent on temperature (`re’ = kT/qIE`). As temperature rises, `re’` increases, which can slightly decrease the gain of a bypassed amplifier.
• Collector Resistor (RC): The voltage gain is directly proportional to the value of RC. A larger RC leads to higher gain but also limits the maximum possible output voltage swing (headroom) and increases the output impedance.
• Emitter Resistor (RE): When unbypassed, RE provides negative feedback (emitter degeneration), which stabilizes the gain, increases input impedance, and reduces distortion at the cost of lower overall gain. The choice to bypass it or not is a classic design trade-off.
• Load Resistance (RL): If another stage or a speaker is connected to the output, this “load” resistance appears in parallel with RC for AC signals. This will reduce the total AC collector resistance (`rC = RC || RL`) and lower the overall voltage gain.
• Signal Frequency: The coupling and bypass capacitors have reactances that change with frequency. At very low frequencies, their high reactance can reduce the amplifier’s gain. At very high frequencies, parasitic capacitances within the transistor itself can cause the gain to drop off. To learn more about this, see our article on understanding impedance matching.

Frequently Asked Questions (FAQ)

Why is the voltage gain (Av) negative?

The negative sign indicates a 180-degree phase inversion. When the input AC signal goes positive, the output signal goes negative, and vice-versa. This is a fundamental characteristic of the common-emitter configuration.

What is the purpose of the voltage divider R1 and R2?

R1 and R2 form a voltage divider biasing network. They set a specific, stable DC voltage at the base of the transistor to establish the desired quiescent operating point (Q-point), ensuring the transistor operates in the active region. A voltage divider calculator can help with this part of the design.

What does bypassing the emitter resistor do?

Placing a capacitor in parallel with RE creates a short circuit for AC signals (at mid-band frequencies), while leaving the DC biasing intact. This removes RE from the AC gain equation, dramatically increasing the voltage gain calculator result. The trade-off is reduced stability and lower input impedance.

How accurate is the `re’ = 26mV / IE` formula?

This is a widely used and effective approximation for silicon bipolar junction transistors at room temperature (~25°C). The theoretical value is `VT / IE`, where VT (the thermal voltage) is about 25.85mV at 300K. For most practical purposes, 26mV is sufficient.

Why is input impedance important?

Input impedance determines how much current the amplifier will draw from the signal source. For maximum voltage transfer, the amplifier’s input impedance should be much higher than the source’s output impedance. A low Zin can “load down” the source, reducing the signal level before it even gets amplified. See our guide on small signal analysis for more detail.

What limits the output voltage swing?

The output voltage cannot swing higher than the supply voltage (Vcc) or lower than a certain saturation voltage (Vce_sat, typically ~0.2V) plus the voltage across RE. Exceeding these limits causes the signal to be “clipped,” resulting in distortion.

Can I use this calculator for a PNP transistor?

Yes, the math is identical. However, for a PNP transistor, the power supply (Vcc) would be negative, and all DC currents and voltages would have reversed polarities. The small-signal AC characteristics behave the same way.

What does the output impedance (Zout) signify?

Output impedance represents the internal resistance of the amplifier as seen from the output terminal. For effective signal transfer to a subsequent stage, the Zout of the amplifier should ideally be much lower than the input impedance of the next stage (the load). In a simple CE amplifier, Zout is approximately equal to the collector resistor, RC.

Related Tools and Internal Resources

Explore these related calculators and articles to deepen your understanding of electronic circuits.

• Ohm’s Law Calculator: Quickly calculate voltage, current, resistance, and power.
• Understanding BJT Transistors: A foundational guide to how bipolar junction transistors work.
• Voltage Divider Calculator: Essential for designing stable biasing circuits.
• How to Read Resistor Color Codes: A practical guide for breadboarding your circuits.
• Op-Amp Gain Calculator: Explore another common type of amplifier circuit.
• Understanding Impedance Matching: Learn why matching source and load impedances is critical.