Signals and signal sources
A 600 Ω microphone connected to a 600 Ω input loses half of its signal before the amplifier does anything. Choosing an amplifier starts with looking at the source.
01The signal and its source
An amplifier never works alone: it takes the signal from a source —a microphone, a sensor, an antenna, the output of another circuit— and delivers it to a load. How well or badly it performs depends as much on those two ends as on the amplifier itself. That is why the study of amplifiers starts by modeling the source. The description of signals in time and in frequency is in signals in circuits; here the source matters as a circuit.
Every linear source can be replaced by a Thévenin equivalent —a voltage source \( v_s \) in series with a resistance \( R_s \)— or a Norton equivalent —a current source \( i_s = v_s / R_s \) in parallel with the same \( R_s \)—. The two models are equivalent; you choose the one that better describes what the source does: a microphone behaves like a voltage source, a photodiode like a current source.
02Typical sources
| Source | Typical signal | Source resistance | Modeled as |
|---|---|---|---|
| Dynamic microphone | A few millivolts | 150 to 600 Ω | Voltage |
| Electret microphone, with its JFET | Tens of millivolts | 1 to 2 kΩ | Voltage |
| Type K thermocouple | About 41 µV per degree | A few ohms | Voltage |
| Electrocardiogram electrodes | Around 1 mV | Kilohms to megohms, variable | Voltage |
| Photodiode | Nanoamperes to microamperes | Very high | Current |
| Receiving antenna | Microvolts | 50 or 75 Ω | Voltage, matched |
| Professional audio line | 1.23 V rms (+4 dBu) | Tens of ohms | Voltage |
The source resistance also sets a noise floor: every resistance generates thermal noise \( v_n = \sqrt{4 k T R B} \). A 1 kΩ source, over the 20 kHz of audio and at room temperature, already brings about 0.58 µV rms that no amplifier can remove.
03Decibels
The signals in a system span many orders of magnitude, from the microvolts of the antenna to the volts of the loudspeaker. That is why they are measured in decibels, a logarithmic scale of ratios:
With a fixed reference, the decibel becomes an absolute unit:
| Unit | Reference | Use |
|---|---|---|
| dBm | 1 mW | Radio frequency and telecommunications |
| dBu | 0.775 V rms, the voltage that gives 1 mW in 600 Ω | Professional audio |
| dBV | 1 V rms | Consumer audio (−10 dBV = 0.316 V) |
| dBµV | 1 µV | Signal levels at antennas and in electromagnetic compatibility |
04The loaded source
When the source is connected to the input of an amplifier, of resistance \( R_{in} \), a voltage divider is formed. The voltage that actually arrives is
This gives three criteria, depending on what you want to transfer:
- Voltage: \( R_{in} \gg R_s \). This is the case for almost all audio and instrumentation: an input ten or more times larger than the source.
- Current: \( R_{in} \ll R_s \). A photodiode is connected to a transimpedance amplifier, whose input is almost a short circuit.
- Power: \( R_{in} = R_s \). This is the matching used in radio frequency, where everything is 50 Ω so that there are no reflections and the maximum power is transferred.
Besides its resistance, every input and every cable has capacitance. Together with the source resistance it forms a low-pass filter, with cutoff frequency \( f_c = 1 / (2\pi\, (R_s \parallel R_{in})\, C_{in}) \): a high-impedance source loses its high frequencies in a long cable.
A source with its internal resistance connected to an input with resistance and capacitance in parallel (those of the cable and of the amplifier). The graph shows how much signal arrives at each frequency, in decibels relative to the open-circuit voltage of the source.
05The four types of amplifier
Depending on which quantity it takes from the source and which quantity it delivers to the load, an ideal amplifier belongs to one of four types. Their ideal input and output resistances follow from the same loading argument:
| Type | Input → output | Gain | Ideal \( R_{in} \) | Ideal \( R_{out} \) |
|---|---|---|---|---|
| Voltage | voltage → voltage | V/V | Infinite | Zero |
| Current | current → current | A/A | Zero | Infinite |
| Transconductance | voltage → current | A/V (siemens) | Infinite | Infinite |
| Transresistance | current → voltage | V/A (ohms) | Zero | Zero |
A transistor on its own is, by nature, a transconductance amplifier: its input is a voltage and its output a current. The circuits in the following units surround it with resistors and other transistors to turn it into whichever type is needed.
06In the lab
Measure the open-circuit voltage of a function generator and then with a 50 Ω load resistor. Calculate its internal resistance using the divider.
With a generator in series with 100 kΩ and 3 m of coaxial cable to the oscilloscope, sweep the frequency and find the −3 dB point. Estimate the capacitance of the cable per meter.
Measure the line output of a sound card and of a media player, and express it in dBV and in dBu.
07Common mistakes
- Forgetting the source resistance. The open-circuit voltage is not the one that arrives.
- Matching impedances in audio. Half the voltage is lost for no reason: in audio the aim is \( R_{in} \gg R_s \).
- Adding power decibels and voltage decibels as if they were the same. 20 log for voltages, 10 log for powers.
- Ignoring the cable capacitance with high-impedance sources. It cuts the high frequencies.
08Self-assessment
How many decibels are lost if \( R_{in} = R_s \)?
6 dB: half the voltage arrives.
How many volts is +4 dBu?
\( 0.775 \times 10^{4/20} \approx 1.23 \) V rms.
Which type of amplifier suits a photodiode?
A transresistance amplifier: current input, with a very low resistance, and voltage output.
A 50 kΩ source with 200 pF of cable and a very high input resistance: where does it cut off?
\( 1/(2\pi \times 50\,000 \times 200 \times 10^{-12}) \approx 15.9 \) kHz.
09Further reading
- Adel S. Sedra and Kenneth C. Smith. Microelectronic Circuits. 7th ed., Oxford University Press, 2014. The first chapter presents the sources and the four types of amplifier with this same loading argument.
- Paul Horowitz and Winfield Hill. The Art of Electronics. 3rd ed., Cambridge University Press, 2015. Input and output impedances, decibels and real sources, from a practical point of view.
- Douglas Self. Small Signal Audio Design. 3rd ed., Focal Press, 2020. Levels, impedances and noise of real audio sources, with measurements.