Differential Pair Configurations

Modes

Common Mode:

• Definition: Common mode refers to a signal that appears simultaneously and equally at both inputs of the long tail pair. It can be thought of as a "background" signal that doesn't carry any useful information.

• Effect on the output: Ideally, a long tail pair rejects common-mode signals. This means the output should remain constant regardless of any common-mode input voltage.

• Reasons for rejection: The symmetry of the circuit, with identical transistors and matched components, contributes to common-mode rejection. The shared current source also plays a role in canceling out common-mode currents.

• Importance: Common-mode rejection is crucial in various applications, particularly when dealing with noisy environments or when amplifying small differential signals.

Single-Ended Mode:

• Definition: Single-ended mode refers to a signal applied to only one input of the long tail pair while the other input is held at a constant voltage (usually ground).

• Effect on the output: The output voltage will change in response to the single-ended input voltage. The gain of the long tail pair in single-ended mode is typically half of the differential mode gain.

• Applications: Single-ended mode is often used for converting voltage signals from single-ended sources to differential signals, which can be further processed by differential amplifiers.

Differential Mode:

• Definition: Differential mode refers to the difference between the two input voltages applied to the long tail pair. This difference represents the actual information being amplified.

• Effect on the output: The output voltage will amplify the differential input voltage by a factor of the differential mode gain.

• Importance: Differential mode is the primary operating mode of the long tail pair, as it allows for amplification of the desired signal while rejecting common-mode noise.

Impedance Matters

Emitter followers have a very low output impedance, often just a few 10's of ohms or less.

An emitter follower will actively resist attempts to change the voltage at its emitter. It actively creates a low impedance using the transistor current gain. 

This means in Differential or Single Ended mode each emitter follower drives an extremely low impedance load (the other transistor's emitter), such that it is almost as if each emitter is connected to ground. The input impedance of the differential pair then is only slightly higher than a common emitter amplifier (not particularly high.)

In Common mode with 2 equal voltages inputted at each base the circuit basically acts as 2 emitter followers in parallel, with the very high input impedance you would expect and allowing large value biasing resistors to be used (common mode biasing.)

Response to Inputs Curve

A single transistor common emitter stage exhibits an exponential response curve to input voltage changes. In the differiental pair the 2 exponential response curves of the 2 transistors counter each other resulting in tanh (hyperbolic tangent) response curve. 

Advantages of the Tanh Curve:

• Smooth Transition: The gradual rise and saturation of the tanh function provide a smooth transition between different operating states, minimizing distortion and unwanted artifacts.

• Wide Input Range: The tanh curve allows a wide range of input voltages to be handled without exceeding the maximum output current.

• Gain Reduction with Amplitude: The tanh curve causes a gradual reduction in gain with increasing input signal amplitude.

The Miller Effect

The Miller effect occurs in circuits with high impedance input nodes and low impedance output nodes. It essentially amplifies the capacitance between the input and output nodes, making it appear larger than its actual value. This "virtual" capacitance is given by:

C_m = A * Ccb

where:

C_m is the Miller capacitance

A is the voltage gain of the stage

Ccb is the collector-base capacitance of the transistor

In the differential pair, the Miller effect can amplify the base-collector capacitance (Cbc) of either or both transistors, increasing the input capacitance of the differential pair, leading to several consequences:

Reduced gain at high frequencies: As the frequency increases, the reactance of the Miller capacitance decreases, shunting more current away from the collector and reducing gain. This can severely limit the bandwidth of the circuit.

Increased phase shift: The Miller capacitance also introduces additional phase shift at high frequencies, potentially leading to instability if not compensated for.

Decreased input impedance: The amplified input capacitance lowers the input impedance of the LTP.

Current biasing the differential pair.

It is possible to current bias the differential pair if exact knowledge of the current through each transistor is not required. This is not suitable for high power applications where thermal runaway could be a problem but is fine for low power operation.

Unwanted Oscillation

This is most like to happen with inductive inputs. One solution is a stopper resistor connecting the input to the inductor. For impedance matching into a differential pair it is better to use a capacitor divider circuit than an inductive matching circuit.

Reduced Forms of the Differential Pair

It is possible to reduce the component count needed for the differential pair while still keeping the transistor within the datasheet defined active region. There is increased collector base capacitance, some gain reduction and limited output voltage swing. Nevertheless such circuits can work well.