E- 4kT R ES= 4kTR (27.11) E2 =4kTR where k is Boltzmanns constant and T is absolute temperature(Kelvin). To obtain the total output noise, one lust multiply the Eout expression of Eq (27. 10)by the noise bandwidth of the circuit, which typically is equal to /2 times the -3 dB signal bandwidth, for a single-pole response system [ Kennedy, 1988] SPICE Computer Models The use of op amps can be considerably simplified by computer-aided analysis using the program SPICE. SPICE originated with the University of California, Berkeley, in 1975 [Nagel, 1975], although more recent user-friendly commercial versions are now available such as HSPICE, HPSPICE, IS-SPICE, PSPICe, and ZSPiCe, to mention a few of those most widely used A simple macromodel for a near-ideal op amp could be simply stated with the SPICe subcircuit file(* indicates a comment that is not processed by the file) SUBCKT IDEALOA 123 "A near-ideal op amp: (1)is noninv,(2)is inv, and(3)is output. RIN 12 1E12 El(3,0)(1,2)1E8 ENDS IDEALOA (27.12) The circuit model for IDEALOA would appear as in Fig. 27. 4(a). A more complete model, but not including nonideal offset effects, could be constructed for the 741 op amp as the subcircuit file OA741, shown in Fig.274(b) SUBCKT OA741126 *A linear model for the 741 op amp: (1)is noninv,(2)is inv, and (6)is output. RiN= 2MEG, AOL =200,000, ROUT=75 ohm, Dominant open-loop pole at 5 Hz, gain-bandwidth product *is 1 mhz RIN 12 2MEG E(3,0)(1,2)2E5 Rl34100K C1 400.318UF: RI X CI= 5HZPOLE E2(5,0)(4,0)1.0 ROUT 75 ENDS OA741 (27.13) The most widely used op amp macromodel that includes dc offset effects is the Boyle model Boyle et al, 1974]. Most op amp manufacturers use this model, usually with additions to add more poles(and perha zeroes). The various resistor and capacitor values, as well as transistor, and current and voltage generator, values are intimately related to the specifications of the op amp, as shown earlier in the nonideal model of Fig. 27.3 The appropriate equations are too involved to list here; instead, the interested reader is referred to the article by Boyle in the listed references. The Boyle model does not accurately model noise effects, nor does it fully gA more circuits-oriented approach to modeling op amps can be obtained if the input transistors are removed nodel psrr and cmrr effects and a model formed by using passive components along with both fixed and dependent voltage and current sources. Such a model is shown in Fig. 27.5. This model not only includes all the basic nonideal effects of the op amp, allowing for multiple poles and zeroes, but can also accurately include ENV and ENI noise effects e 2000 by CRC Press LLC© 2000 by CRC Press LLC (27.11) where k is Boltzmann’s constant and T is absolute temperature (°Kelvin). To obtain the total output noise, one must multiply the E2 out expression of Eq. (27.10) by the noise bandwidth of the circuit, which typically is equal to p/2 times the –3 dB signal bandwidth, for a single-pole response system [Kennedy, 1988]. SPICE Computer Models The use of op amps can be considerably simplified by computer-aided analysis using the program SPICE. SPICE originated with the University of California, Berkeley, in 1975 [Nagel, 1975], although more recent user-friendly commercial versions are now available such as HSPICE, HPSPICE, IS-SPICE, PSPICE, and ZSPICE, to mention a few of those most widely used. A simple macromodel for a near-ideal op amp could be simply stated with the SPICE subcircuit file (* indicates a comment that is not processed by the file) .SUBCKT IDEALOA 1 2 3 *A near-ideal op amp: (1) is noninv, (2) is inv, and (3) is output. RIN 1 2 1E12 E1 (3, 0) (1, 2) 1E8 .ENDS IDEALOA (27.12) The circuit model for IDEALOA would appear as in Fig. 27.4(a). A more complete model, but not including nonideal offset effects, could be constructed for the 741 op amp as the subcircuit file OA741, shown in Fig. 27.4(b). .SUBCKT OA741 1 2 6 *A linear model for the 741 op amp: (1) is noninv, (2) is inv, and *(6) is output. RIN = 2MEG, AOL = 200,000, ROUT = 75 ohm, *Dominant open - loop pole at 5 Hz, gain - bandwidth product *is 1 MHz. RIN 1 2 2MEG E1 (3, 0) (1, 2) 2E5 R1 3 4 100K C1 4 0 0.318UF ; R1 2 C1 = 5HZPOLE E2 (5, 0) (4, 0) 1.0 ROUT 5 6 75 .ENDS OA741 (27.13) The most widely used op amp macromodel that includes dc offset effects is the Boyle model [Boyle et al., 1974]. Most op amp manufacturers use this model, usually with additions to add more poles (and perhaps zeroes). The various resistor and capacitor values, as well as transistor, and current and voltage generator, values are intimately related to the specifications of the op amp, as shown earlier in the nonideal model of Fig. 27.3. The appropriate equations are too involved to list here; instead, the interested reader is referred to the article by Boyle in the listed references. The Boyle model does not accurately model noise effects, nor does it fully model PSRR and CMRR effects. A more circuits-oriented approach to modeling op amps can be obtained if the input transistors are removed and a model formed by using passive components along with both fixed and dependent voltage and current sources. Such a model is shown in Fig. 27.5. This model not only includes all the basic nonideal effects of the op amp, allowing for multiple poles and zeroes, but can also accurately include ENV and ENI noise effects. E kT R E kT R EF F kT R 1 2 1 2 2 2 2 4 4 4 = = =