page_title: Differential amplifier
section_title: Symmetrical feedback network eliminates common-mode gain and common-mode bias
hierarchical_section_title: Differential amplifier / Applications / Symmetrical feedback network eliminates common-mode gain and common-mode bias
context_page_description: A differential amplifier is a type of electronic amplifier that amplifies the difference between two input voltages but suppresses any voltage common to the two inputs. It is an analog circuit with two inputs and and one output in which the output is ideally proportional to the difference between the two voltages
  where is the gain of the amplifier.
  Single amplifiers are usually implemented by either adding the appropriate feedback resistors to a standard op-amp, or with a dedicated IC containing internal feedback resistors. It is also a common sub-component of larger integrated circuits handling analog signals.
context_section_description: In case the operational amplifier's (non-ideal) input bias current or differential input impedance are a significant effect, one can select a feedback network that improves the effect of common-mode input signal and bias. In Figure 6, current generators model the input bias current at each terminal; I⁺b and I⁻b represent the input bias current at terminals V⁺ and V⁻, respectively.
  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⁻//.
  These equations undergo a great simplification if 
  resulting in the relation,
  which implies that the closed-loop gain for the differential signal is V⁺ᵢₙ - V⁻ᵢₙ, but the common-mode gain is identically zero. 
  It also implies that the common-mode input bias current has cancelled out, leaving only the input offset current IΔb = 'I⁺b - 'I⁻b still present, and with a coefficient of Rᵢ. It is as if the input offset current is equivalent to an input offset voltage acting across an input resistance Rᵢ, which is the source resistance of the feedback network into the input terminals. 
  Finally, as long as the open-loop voltage gain Aₒₗ is much larger than unity, the closed-loop voltage gain is Rf / Rᵢ, the value one would obtain through the rule-of-thumb analysis known as "virtual ground".
caption: Figure 6: Differential amplifier with non-ideal op-amp: input bias current and differential input impedance