OPERATIONAL AMPLIFIERS An amplifier is a signal conditioning device which alters an analog signal in a particular manner which can be described by the relationship: ( ) [ ( )]out int = h t (6.43)EE where Eo is the output voltage, Ei is the input voltage, and h is some mathematical relationship. (a transfer function!) For many amplifiers, h = constant and the amplifier only alters the gain of the signal. Giving: ( ) ( )out vo inE t A E t where the open loop gain of the amplifier is Avo. ( ) [ ( ) ( )]21oiivot = A t - tE E EThe Ideal Op Amp Figure 1. Equivalent circuit for an ideal operational amplifier. 1. The voltage gain is infinite: Avo = ∞ 2. The input resistance is infinite: rin = ∞ 3. The output resistance is zero: ro = 0 4. The bandwidth is infinite: BW = ∞ 5. There is zero input offset voltage: EO = 0 if Ein = 0 AXIOMS 1. The differential input voltage is zero. 2. There is no current flow into either input terminal 3. With the loop closed, the (-) input will be driven to the potential of the (+), or reference, input.Some Basic Amplifying Circuits 1. the inverting configuration 2. the noninverting configuration 3. the differential configuration (combination of 1. and 2.) 4. the summing Inverter configuration 5. the Integrator configuration 6. the Differentiator configuration 7. the Voltage Follower configuration Standard Op-Amp Schematic SymbolIf we operate the amplifier in a closed loop feedback mode we can analyze the resulting circuit based on some simplifying assumptions. Consider the circuit shown in Figure 6.24a1, 6.21a2,3, 6.20a4. We will assume that the open loop gain is infinite, that the input impedance is infinite, and that the output impedance is zero. For infinite input impedance, the current flowing into the amplifier becomes zero. 22212oiif1221oi2oii21oi2 - E E E = = iRR + RR = EER - = /A = 0E E E + RR = EEROperationalAmplifiers.doc Page 1 of 16 11/19/2008 1:30 PM The closed loop gain is given by o 2 1i2 + E R RG = = (6.46)ER Remarkably, the closed loop gain is dependent only on the two resistances and not on the amplifier gain. Now consider the circuit shown in Figure 6.21 (e) 12(note can be 0)R21iAf o AR2B1IA B o Aio2oid [ - ]EE = C [ - ] = - = - iI E EdtR = = 0 iER - = /A = 0, so = 0E E E EdEC = - EdtR1 = - dtEERC (6.52) Note the error in Eq. (6.52) in the text in the First Edition. By combining the elements shown in Figure 6.241, 6.212,3, 6.204, we can perform manyOperationalAmplifiers.doc Page 2 of 16 11/19/2008 1:30 PM mathematical operations, hence the term operational amplifier. Only a rudimentary knowledge of electronics is required to design operational amplifier circuits. The performance of the circuit depends only on the circuit elements and is independent of the gain of the operational amplifier, as long as it remains constant. Thus, operational amplifiers can be made quite inexpensively.OperationalAmplifiers.doc Page 3 of 16 11/19/2008 1:30 PM Summary of Inverting Amplifier Characteristics 1. Gain = finRR, unlimited in range (Rf may be 0 for 0 gain, may in infinite). 2. Input Impedance = Rin. 3. If = Iin, regardless of Rf (Is=0!). 4. Summing point is a virtual ground at the same potential as the (+) input.OperationalAmplifiers.doc Page 1 of 16 11/19/2008 1:30 PM Inverting AmplifierOperationalAmplifiers.doc Page 1 of 16 11/19/2008 1:30 PM Summary of Non-Inverting Op Amp 1. Gain = in finRRR lower limit of unity gain where Rin = ∞, or Rf = 0. 2. Input Impedance = ∞ 3. If = Iin, regardless of RfOperationalAmplifiers.doc Page 1 of 16 11/19/2008 1:30 PM Non-Inverting Op AmpOperationalAmplifiers.doc Page 1 of 16 11/19/2008 1:30 PM Summary of Differential Op Amp 1. Differential-Mode Gain (Ein1 ≠ Ein2) 12foin in inREE E ROperationalAmplifiers.doc Page 2 of 16 11/19/2008 1:30 PM 2. Common-Mode Gain (Ein1 = Ein2) a. When ,0ffin inRRRR b. When ,f f f in f inin in in in in fR R R R R RR R R R R R c. In terms of resistor match (worst case) 4fin fRRR where δ = fractional unbalance of resistors (i.e. 1%=0.01) and Rin and Rf are the nominal resistance values.OperationalAmplifiers.doc Page 1 of 16 11/19/2008 1:30 PMOperationalAmplifiers.doc Page 1 of 16 11/19/2008 1:30
View Full Document
Unlocking...