Developing equations for fully differential amplifiers

Fully differential amplifiers and op amps are similar, but they are not identical. You must consider the input voltages and both output voltages when developing fully-differential-amplifier transfer equations. (This column later addresses the development of the com- mon-mode-voltage equation.) You use the fully-differential-amplifier circuit in Figure 1 to develop the transfer equations. Equation 1 is the amplifier equation, where a is the amplifier gain, and equations 2 and 3 are the amplifier-input-node equations.

V_OUT+–V_OUT–=a(V_P–V_N). EQUATION 1

EQUATION 2

EQUATION 3

Substituting equations 2 and 3 into Equation 1, combining terms, and assuming that R₁=R₃ and R₂=R₄ yields Equation 4:

EQUATION 4

When a is much greater than (R₁+R₂), Equation 4 reduces to Equation 5:

EQUATION 5

When you use both inputs, the circuit functions as a differential-input/differential-output amplifier. When you use one input (either input, with the remaining input grounded), the circuit functions as a single-ended-input/differential-output amplifier. Equation 5 illustrates the ease of making the single-ended-to-differential-signal conversion: Just connect four resistors, and you obtain signal gain by manipulating the R₂/R₁ resistor ratio. The fully differential amplifier eliminates the need for complex two- and three-op-amp versions of single-ended-to-differential-output converters. It has several other advantages over op-amp configurations: higher speed, cheaper cost, smaller space requirement, and lower power consumption.

You calculate the common-mode output voltage, V_OCM, with the aid of Equation 6 (Reference 1):

EQUATION 6

Notice that the common-mode output voltage goes to zero when R₁ and R₂ match. It is best to implement the fully differential amplifier with matched resistors to eliminate common-mode voltages. Film resistors are the best source of inexpensive matched resistors. Low-cost matched-film-resistor sets may become readily available in different gain configurations as the popularity of fully differential amplifiers increases.

Author Information

Ron Mancini is staff scientist at Texas Instruments. You can reach him at 1-352-569-9401, rmancini@ti.com.