Differential amplifier

1. Introduction to operational amplifiers
Operational Amplifiers or Op-amps are one of the basic elements of Analogue Electronic Circuits. They are linear devices that commonly used in signal conditioning, filtering or in mathematical operations for example adding, subtracting, integrating or differentiating.

An op-amp is a voltage amplifying device used with external feedback components for instance resistors and capacitors between output and input terminals. The above mentioned feedback components are to determine the function of the amplifier, that could be resistive, capacitive or both. This three-terminal device consists also of two high impedance inputs: Inverting Input (-), Non-inverting Input (+) and output port which can either sinks or sources voltage and current. There can be four different classifications of operational amplifier gain:


 * Voltage –Voltage “in” and Voltage “out”
 * Current – Current “in” and Current “out”
 * Transconductance – Voltage “in” and Current “out”
 * Transresistance – Current “in” and Voltage “out”



2. Differential Amplifiers
Why and where use integrated fully-differential amplifiers?


 * Immunity to external noise is increased
 * Best for low-voltage systems
 * Easy to use in integrated circuit
 * Even-order harmonics reduced
 * ECG (Electrocardiography - is the process of recording the electrical activity of the heart over a period of time)
 * EEG (Electroencephalography - is an electrophysiological monitoring method to record electrical activity of the brain)
 * EMG (Electromyography - technique for evaluating and recording the electrical activity produced by skeletal muscles )



The differential amplifier has a unique feature that is, it amplifies the voltage difference between two input signals unlike the single-ended which amplify a single input signal. A principle application is to eliminate the noise (common-mode fluctuating voltage). It may be also configurated to operate as a single-ended amplifier by grounding one of the inputs. An integrated, fully-differential amplifier architecturally resembles a standard, voltage-feedback operational amplifier. Both have differential inputs, however a standard operational amplifier's output is single-ended and the other's is differential. Due to the above mentioned fact, in the differential amplifier the output common-mode voltage can be controlled independently of the differential voltage and in a standard one the signal and output common-mode voltage are the same thing. It is also worth mentioning that a fully-differential amplifier has multiple feedback paths. Below there is a figure presenting differences between a fully-differential and a standard operational amplifier.



2.1. Long-tailed pair
The basic differential pair amplifier is composed of at least two identical transistors. LTP (long-tailed pair) or emitter coupled (source coupled) pair, is a pair of transistors that share source node supplied from constant current source. Large value resistor is connected to the negative supply, which develops a voltage drop – relative to the amplitude of the input signal. This configuration gives the circuit configuration its name - a long tail. The resistor that is in high value resembles a current source. Additionally, the long tail resistor is often replaced by an active current source in many integrated circuits.

2.2. Differential Gain
Gain of an amplifier is defined as VOUT/VIN. For the special case of a differential amplifier, the input VIN is the difference between its two input terminals, which is equal to (V1-V2). The output from a differential amplifier is itself often differential.



Where:
 * Vout = output voltage
 * V+in = input voltage on the positive input
 * V-in = input voltage on the negative input
 * Ad = differential gain

Below more accurate representation of gain can be found. It includes both the differential and common mode elements of the output.



Where: Ac = common mode gain

Sources:

http://www.electronics-tutorials.ws/opamp/opamp_5.html

https://books.google.pl/books?id=0yJ3blaI7b8C&pg=PA157&lpg=PA157&dq=Differential+amplifier+for+dummies&source=bl&ots=13mLh_lt9y&sig=KNT9CqYcrmd1tX5PGW0MxgRzZuc&hl=pl&sa=X&ved=0ahUKEwjv37CysKnJAhWHXCwKHZBHCx0Q6AEIUDAG#v=snippet&q=differential&f=false

https://en.wikipedia.org/wiki/Differential_amplifier#Long-tailed_pair

http://www.allaboutcircuits.com/textbook/semiconductors/chpt-8/negative-feedback/

http://www.ecircuitcenter.com/Circuits/opdif/opdif.htm

https://en.wikipedia.org/wiki/Operational_amplifier

http://www.radio-electronics.com/info/circuits/transistor/long-tailed-pair.php

https://wiki.analog.com/university/courses/electronics/text/chapter-12

http://www.ti.com/lit/an/sloa054d/sloa054d.pdf

http://www.bbc.co.uk/schools/gcsebitesize/design/electronics/integratedrev3.shtml