Differential amplifier

It is also a common sub-component of larger integrated circuits handling analog signals.

As differential amplifiers are often used to null out noise or bias voltages that appear at both inputs, a low common-mode gain is usually desired.

The common-mode rejection ratio is defined as In a perfectly symmetric differential amplifier,

The bias points of “long-tail” resistor circuit are largely determined by Ohm's law and less so by active-component characteristics.

The long-tailed pair was developed from earlier knowledge of push–pull circuit techniques and measurement bridges.

[2] An early circuit which closely resembles a long-tailed pair was published by British neurophysiologist Bryan Matthews in 1934,[3] and it seems likely that this was intended to be a true long-tailed pair but was published with a drawing error.

The earliest definite long-tailed pair circuit appears in a patent submitted by Alan Blumlein in 1936.

[4] By the end of the 1930s the topology was well established and had been described by various authors, including Frank Offner (1937),[5] Otto Schmitt (1937)[6] and Jan Friedrich Toennies (1938),[7] and it was particularly used for detection and measurement of physiological impulses.

[8] The long-tailed pair was very successfully used in early British computing, most notably the Pilot ACE model and descendants,[nb 1] Maurice Wilkes’ EDSAC, and probably others designed by people who worked with Blumlein or his peers.

The long-tailed pair has many favorable attributes if used as a switch: largely immune to tube (transistor) variations (of great importance when machines contained 1,000 tubes or more), high gain, gain stability, high input impedance, medium/low output impedance, good clipper (with a not-too-long tail), non-inverting (EDSAC contained no inverters!)

Many computers of this time tried to avoid this problem by using only AC-coupled pulse logic, which made them very large and overly complex (ENIAC: 18,000 tubes for a 20-digit calculator) or unreliable.

The differential pair can be used as an amplifier with a single-ended input if one of the inputs is grounded or fixed to a reference voltage (usually, the other collector is used as a single-ended output) This arrangement can be thought of as cascaded common-collector and common-base stages or as a buffered common-base stage.

[nb 3] The emitter-coupled amplifier is compensated for temperature drifts, VBE is cancelled, and the Miller effect and transistor saturation are avoided.

To explain the circuit operation, four particular modes are isolated below although, in practice, some of them act simultaneously and their effects are superimposed.

The series negative feedback (the emitter degeneration) makes the transistors act as voltage stabilizers; it forces them to adjust their VBE voltages (base currents) to pass the quiescent current through their collector-emitter junctions.

[nb 4] So, due to the negative feedback, the quiescent current depends only slightly on the transistor's β.

So, the sources have to be galvanic (DC) to ensure paths for the biasing current and low resistive enough to not create significant voltage drops across them.

Otherwise, additional DC elements should be connected between the bases and the ground (or the positive power supply).

Bias stability and independence from variations in device parameters can be improved by negative feedback introduced via cathode/emitter resistors with relatively small resistances.

With relatively small collector resistor and moderate overdrive, the emitter can still follow the input signal without saturation.

The collector resistors can be replaced by a current mirror (the top blue section in Fig.

Thus, the difference is twice the individual signal currents (ΔI − (−ΔI) = 2ΔI), and the differential to single-ended conversion is completed without gain losses.

The constant current needed could be produced by connecting an element (resistor) with very high resistance between the shared emitter node and the supply rail (negative for NPN and positive for PNP transistors), but that requires a high supply voltage.

So in more sophisticated designs, an element with high differential (dynamic) resistance approximating a constant current source/sink (the bottom of Fig.

The biasing current will enter directly this base and indirectly (through the input source) the other one.

At differential mode, they behave as common-emitter stages with grounded emitters; so, the input impedances are low.

An op-amp differential amplifier can be built with predictable and stable gain by applying negative feedback (Figure 5).

A long-tailed pair can be used as an analog multiplier with the differential voltage as one input and the biasing current as another.

A differential amplifier is used as the input stage emitter coupled logic gates and as switch.

The Thévenin equivalent for the network driving the V+ terminal has a voltage V+' and impedance R+': while for the network driving the V− terminal: The output of the op-amp is just the open-loop gain Aol times the differential input current i times the differential input impedance 2Rd, therefore where R|| is the average of R+|| and R−||.