Calculator
Formula Used
Compound beta: βD = β1β2 + β1 + β2
Dynamic emitter resistance: re = VT / IE
Darlington internal resistance: re(pair) = re2 + re1 / (β2 + 1)
AC emitter load: RAC = RE || load branch
Base voltage gain: AV(base) = RAC / (RAC + re(pair))
Input resistance: Rin = (βD + 1)(RAC + re(pair))
Source included gain: AV(source) = AV(base) × Rin / (Rin + RS)
How to Use This Calculator
Enter beta values for both transistors. Add the Q2 emitter current, emitter resistor, load resistor, and source resistor.
Set input peak voltage and thermal voltage. Use 25.85 mV for room temperature. Add signal frequency and coupling capacitor value when the load is capacitor coupled.
Press Calculate to view gain, input resistance, output swing, and load power. Use CSV or PDF buttons to export the same calculated result.
Example Data Table
| Case | β1 | β2 | IE2 mA | RE ohm | RL ohm | RS ohm | Expected Use |
|---|---|---|---|---|---|---|---|
| Small signal buffer | 120 | 80 | 10 | 1000 | 2200 | 100 | Audio or sensor driver |
| Higher load resistance | 150 | 100 | 5 | 4700 | 10000 | 50 | Light signal buffering |
| Low load test | 80 | 60 | 20 | 680 | 1000 | 220 | Driver stress check |
Darlington Pair Voltage Gain Guide
Basic Idea
A Darlington pair joins two transistors in one compound device. The emitter of the first transistor drives the base of the second transistor. This connection gives very high current gain. It also creates a useful buffer stage. The voltage gain is normally close to one. Still, it is not exactly one. Internal emitter resistance, load resistance, source resistance, and bias current change the final value.
Why Voltage Gain Matters
Many designers use a Darlington pair as an emitter follower. It does not create large voltage amplification. Its strength is current gain. The circuit lets a weak signal drive a heavier load. A small voltage loss still matters in sensors, audio drivers, relay interfaces, and level shifting stages. A careful gain estimate helps you choose a safe input signal and a sensible load.
Main Design Factors
Current gain depends on both transistor beta values. The combined beta can become very large. Small signal voltage gain depends more on the AC emitter load and dynamic emitter resistance. Higher emitter current lowers dynamic resistance. A larger emitter or load resistance usually moves voltage gain closer to one. Source resistance can reduce the gain seen from the signal generator. A coupling capacitor can also reduce low frequency gain because its reactance adds to the load path.
Practical Interpretation
The calculator separates base to emitter gain from source included gain. This is useful during debugging. A high base gain with a low source gain points to input loading. A low base gain points to a small AC load or high dynamic resistance. The output swing estimate checks whether the chosen input may clip near the supply rails. It is an estimate, not a full simulator.
Good Use Cases
Use this tool during early amplifier design. Use it before building a breadboard. It can compare transistor pairs, bias currents, loads, and source resistances quickly. It also creates records for lab sheets through CSV and PDF exports. For final hardware, test the circuit with real parts. Transistor beta varies with current, temperature, and manufacturing spread. Real boards also include wiring resistance, capacitance, and device limits. Treat the result as a strong design guide before detailed measurement. Keep notes for later design reviews.
FAQs
What is Darlington pair voltage gain?
It is the small signal voltage ratio from input to output. In most emitter follower Darlington circuits, it is close to one. It becomes lower when internal emitter resistance, source resistance, or heavy loading becomes significant.
Why is the gain not exactly one?
The transistors need small internal voltage changes to move current. This internal dynamic emitter resistance creates a small drop. The drop grows when emitter current is low or the AC load is small.
What does compound beta mean?
Compound beta is the combined current gain of both transistors. The calculator uses βD = β1β2 + β1 + β2. This value affects input resistance and source loading.
Should I include source resistance?
Yes, include it when the signal source is not ideal. Source resistance can reduce the voltage that reaches the Darlington input. This lowers the source included gain.
What thermal voltage should I use?
Use about 25.85 mV near room temperature. Change it when temperature matters. Thermal voltage affects the dynamic emitter resistance and therefore changes the small signal gain estimate.
Why add a coupling capacitor?
A coupling capacitor blocks DC but adds reactance at low frequency. That reactance changes the load branch. Low capacitor values can reduce low frequency signal transfer.
Can this replace circuit simulation?
No. It gives a strong small signal estimate. A simulator or bench test is better for distortion, switching behavior, device spread, capacitance, and large signal operation.
What does the swing check show?
It compares the estimated output peak with available supply headroom. If the output peak is too large, the stage may clip. Real transistor saturation and bias limits can change this result.