Gain, Input and Output Impedance
The three most important specifications of any amplifier stage are its gain, its input impedance, and its output impedance. Gain tells you how much larger the output is than the input. Input impedance tells you how much the amplifier loads the stage or source that drives it. Output impedance tells you how well the amplifier can drive the next stage without losing signal at the interface. Together these three parameters determine how well stages can be connected together into a working system — and in radio design, getting them right is the difference between a sensitive, selective receiver and one that is mediocre.
You have already seen gain and impedance formulas for the three basic BJT configurations. In this lesson you will consolidate that knowledge, learn to express gain in decibels (the language of radio engineering), and most importantly, learn how gain and impedance interact when multiple stages are cascaded — connected in series — to build up the total gain of a receiver front end, an IF chain, or a power amplifier driver chain.
Three cascaded amplifier stages. Gains in dB simply add: 20 + 15 + 10 = 45 dB total gain. Signal levels in dBm are annotated at each stage — this is how receiver system designers track signal flow from antenna to detector.
View LargerVoltage Gain
Voltage gain is the ratio of output voltage to input voltage. If you apply 10 mV to the input and measure 500 mV at the output, the voltage gain is 500/10 = 50. Voltage gain has no units — it is a dimensionless ratio. It can be greater than 1 (amplification), equal to 1 (buffer), or less than 1 (attenuation).
Av = Vout / Vin
For a common emitter stage (with bypass): Av = RC / re
For a common emitter stage (without bypass): Av = RC / RE
For a common collector stage: Av ≈ 1
For a common base stage: Av = RC / re (positive, non-inverting)
The sign of the voltage gain indicates phase. A negative gain (CE stage) means the output is inverted with respect to the input. A positive gain means the output is in phase. When you compute the gain in decibels, you always take the absolute value of Av — dB gain is always expressed as a positive number for amplification (or negative for attenuation), regardless of phase.
Current Gain
Current gain is the ratio of output current to input current. For a BJT in common emitter configuration, the current gain is the transistor's beta (β or hFE) — the ratio of collector current to base current. Beta is specified on the transistor's datasheet and typically ranges from 50 to several hundred for common small-signal transistors.
Ai = Iout / Iin
Common emitter: Ai = β (hFE)
Common base: Ai = α = β/(β+1) ≈ 1
Common collector: Ai = β+1 ≈ β (high — emitter current includes base current)
Note that the common collector stage has the highest current gain of all three configurations. This is why the emitter follower can deliver large currents to a load from a small input current — it is a current amplifier.
Power Gain
Power gain is the ratio of output power to input power. Since power = voltage × current, the power gain is related to both voltage gain and current gain:
Ap = Pout / Pin = (Vout × Iout) / (Vin × Iin) = Av × Ai
A common emitter stage with voltage gain 50 and current gain 100 has a power gain of 5000. Expressed in decibels: 10 × log₁₀(5000) = 37 dB. The CE stage amplifies power by a factor of 5000, turning a tiny input signal power into a much larger output signal power — the energy for this comes from the DC supply.
Gain in Decibels
Decibels are the universal language of RF engineering. You learned about dB in Module 2. For amplifiers, the conversion rules are:
Av(dB) = 20 × log₁₀(|Av|)
Power gain in dB:
Ap(dB) = 10 × log₁₀(Ap)
Converting back:
Av = 10^(Av(dB)/20)
Ap = 10^(Ap(dB)/10)
Why do voltage and power use different multipliers (20 vs 10)? Because power is proportional to the square of voltage (P = V²/R). Taking the log of V² gives 2 × log V, which is why the coefficient is 2 × 10 = 20 for voltage ratios. When comparing equal impedances (which is the standard assumption in RF work), voltage ratio in dB = power ratio in dB.
| Linear Voltage Gain | dB (voltage) | What it means |
|---|---|---|
| 1 | 0 dB | No gain (buffer) |
| 2 | 6 dB | Voltage doubles |
| 10 | 20 dB | Voltage × 10 |
| 100 | 40 dB | Voltage × 100 |
| 1000 | 60 dB | Voltage × 1000 |
| 0.5 | −6 dB | Half voltage (6 dB attenuation) |
| 0.707 | −3 dB | Half power (3 dB bandwidth point) |
Voltage Gain in dB Calculator
Convert between linear voltage gain (Av) and gain in decibels. Enter either the linear gain or the dB value to convert.
Power Gain in dB Calculator
Convert between linear power gain (Ap = Pout/Pin) and power gain in decibels. Also calculates from input and output power in watts or milliwatts.
Cascaded Stages
When amplifier stages are connected in series — the output of stage 1 feeds the input of stage 2, which feeds stage 3, and so on — the total gain is found by multiplying the individual linear gains, or equivalently, by adding the individual dB gains. This is one of the most powerful reasons to work in decibels: addition is far easier than multiplication, especially when dealing with many stages.
Total Av (linear) = Av1 × Av2 × Av3 × ... × Avn
Total gain (dB) = G1(dB) + G2(dB) + G3(dB) + ... + Gn(dB)
- First IF filter: −3 dB (insertion loss)
- First IF amplifier: +26 dB
- Second IF filter: −4 dB
- Second IF amplifier: +26 dB
- Third IF filter: −6 dB
- AGC amplifier: +20 dB (at maximum gain)
A −100 dBm signal from the mixer would exit the IF chain at −100 + 59 = −41 dBm. The detector circuit might need −10 dBm minimum, so this chain provides more than enough gain with 31 dB of AGC range remaining before the signal reaches the detector at maximum level.
Cascaded Amplifier Gain Calculator
Enter the gain (in dB) of up to 8 cascaded stages (use negative values for attenuators or filters with insertion loss). Also enter an input signal level in dBm to track the signal level through the chain.
Impedance and Inter-Stage Matching
Gain calculations tell you how much a stage amplifies in isolation. But in a real circuit, stages are connected together and their impedances interact. Whenever the output impedance of one stage is connected to the input impedance of the next, a voltage divider is formed — and unless the impedances are well-matched, some of the available signal is lost at the interface.
The voltage actually delivered to the input of the second stage is:
V_in2 = V_out1 × Zin2 / (Zout1 + Zin2)
Loading loss (dB) = 20 × log₁₀(Zin2 / (Zout1 + Zin2))
Voltage at input of stage 2 = V_out1 × 1100 / (2200 + 1100) = V_out1 × 0.333
Loading loss = 20 × log₁₀(0.333) = −9.5 dB
Nearly 10 dB of gain is lost at the interface between these two stages! If stage 1 had a gain of 26 dB but feeds a stage with similar input impedance, the effective gain is only 26 − 9.5 = 16.5 dB. This is why impedance matching between stages matters — and why an emitter follower buffer is often inserted between stages to transform the impedance and eliminate this loading loss.
In RF systems operating at a defined characteristic impedance (almost always 50 Ω), inter-stage matching is handled by designing every output and input at 50 Ω, so the loading factor is always 50/(50+50) = 0.5, which is −6 dB at every interface. This loss is accounted for in the gain specification of each block. Professional RF gain budgets include insertion loss at every junction, and the gain of each amplifier block is specified into 50 Ω loaded conditions.
Inter-stage loading. When Stage 1's output impedance is comparable to Stage 2's input impedance, a significant fraction of the signal is lost at the interface. Matching these impedances (or using a buffer) eliminates this loss.
View LargerWorked Example: HF Receiver Signal Chain
Here is a complete gain budget analysis for a simple HF receiver chain, tracking the signal from a −100 dBm (10 µV into 50 Ω) antenna input to the detector.
| Stage | Gain (dB) | Signal Level (dBm) | Notes |
|---|---|---|---|
| Antenna input | — | −100 | 10 µV into 50 Ω = −100 dBm |
| Bandpass filter | −2 | −102 | Coil loss, insertion loss |
| LNA (cascode preamp) | +15 | −87 | Low noise figure, 50 Ω in/out |
| First mixer | −6 | −93 | Typical diode ring conversion loss |
| First IF filter (9 MHz) | −3 | −96 | Crystal filter insertion loss |
| IF amplifier × 3 | +60 | −36 | Three 20 dB stages |
| AGC attenuation | −20 | −56 | AGC reduces gain with strong signals |
| SSB filter | −4 | −60 | Selectivity filter insertion loss |
| Product detector | 0 | −60 | Needs ≥ −80 dBm to work — plenty of margin |
| Audio amp | +30 | −30 | Drives loudspeaker |
Total gain from antenna to audio output: −2 + 15 − 6 − 3 + 60 − 20 − 4 + 0 + 30 = +70 dB. A −100 dBm signal becomes −30 dBm at the audio amplifier input — plenty of margin above the noise floor of the audio circuits. With a stronger −50 dBm signal, the AGC would increase attenuation further to keep the detector input at a constant level, preventing overloading.
Frequently Asked Questions
Why does power gain use 10×log but voltage gain uses 20×log?
Because power is proportional to the square of voltage. If voltage doubles, power quadruples. log₁₀(V²) = 2 × log₁₀(V). So the voltage gain multiplied by 20 (= 2 × 10) gives the same result in dB as power gain multiplied by 10. For equal source and load impedances this gives the same number, which is why a 6 dB gain means "voltage doubles" and also "power quadruples." When impedances are different, you must be careful: a 6 dB voltage gain into a higher impedance load corresponds to more than a 4× increase in delivered power.
What is the difference between available gain and transducer gain?
Available gain is the maximum gain an amplifier can provide when its input and output are conjugate-matched (source and load impedances are the complex conjugates of the amplifier's input and output impedances). Transducer gain is the actual gain from source to load in a specific circuit with specific source and load impedances. In most ham radio contexts, amplifiers are designed for 50 Ω source and 50 Ω load, and the gain specification on a datasheet assumes this condition. Connecting the amplifier to different impedances will give a different (often lower) gain. This is the practical meaning of "gain depends on impedance matching."
How many dB of gain does a typical HF transceiver receiver have?
A typical modern HF transceiver receiver has a total gain from antenna to loudspeaker of approximately 100–120 dB. This allows a signal as weak as −130 dBm (the thermal noise floor at 14 MHz in a 2.4 kHz SSB bandwidth) to be audible. A −130 dBm signal input with 120 dB of gain emerges at −10 dBm at the loudspeaker drive circuit — a reasonable audio level. This huge gain is distributed across the RF front end, one or two IF stages, an audio amplifier, and sometimes a power audio output stage. AGC reduces the gain by 60–80 dB or more when strong signals are present, preventing overload.
Test Your Knowledge
Answer the questions below to check your understanding. Every answer can be found in the lesson above.