Analog Applications Journal Analog and MixedSignal Products November Analysis of fully - PDF document

48Analog Applications Journal introduced the fully differential amplifiers from Texas OCMOCVV= )VV(A)V()V(NPFOUTOUTŠ=ŠŠ+ 2)V()V(VOUTOUTOCŠ++= )V()V(VOUTOUTODŠŠ+= 2)V()V(VININICŠ++= )V()V(VININIDŠŠ+= Texas Instruments Incorporated VNVPR4R3V+OUTV Ð OUTVOCMR2R1VÐINV+IN ++ÐÐAF Figure 1. Analysis circuit ++ÐÐÐ1Ð\f21Ð\f121 \rVNVPV + OUTV Ð OUTVÐINV+INAF\f\f Figure 2. Block diagram Texas Instruments Incorporated 49Analog Applications Journal By settingandVWith Equations 7 and 8, a block diagram of the main differential amplifier can be constructed, like that shown in With the ÒidealÓ assumption ATo calculate V AA21)(V2)]1)(V()1)(V[(2)(1V2F1F21OCM2IN1IN21OD\b\t\n\f+\f+\fŠ\f+\fŠŠŠ\fŠ+\f+\f= .)()(V2)1)(V()1)(V()V(212OCM2IN1INOUT\f+\f\f++\fŠŠ+\fŠ+Š=Š .AA21A1V2)1)(V()1)(V()(1)V(2F1F2FOCM2IN1IN21OUT\b\t\n\f+\f+\b\t\n\f++\fŠŠ+\fŠ+Š\f+\f=Š .)(V2)1)(V()1)(V()V(211OCM2IN1INOUT\f+\f\f+\fŠŠŠ\fŠ+=+ .AA21A1V2)1)(V()1)(V()(1)V(2F1F1FOCM2IN1IN21OUT\b\t\n\f+\f+\b\t\n\f++\fŠŠŠ\fŠ+\f+\f=+ ,)]1)(V()1)(V[(A)A1(V2)AA2)(V(2IN1INF1FOCM2F1FOUT\fŠŠŠ\fŠ+=\f+Š\f+\f++ .)]1)(V()1)(V[(A)A1)(V()A1)((V2IN1INF1FOUT2FOUT\fŠŠŠ\fŠ+=\f+ŠŠ\f++ .))(V()1)(V(V1OUT1INP\fŠ+\fŠ+= ,))(V()1)(V(V2OUT2INN\f++\fŠŠ= ,R2R1R12\b\t\n+=\f \b\t\n+=\fR4R3R31 .R4R3R3)V(R4R3R4)V(VOUTINP\b\t\n+Š+\b\t\n++= \b\t\n+++\b\t\n+Š=R2R1R1)V(R2R1R2)V(VOUTINN (10)(12)(14)Continued on next page Texas Instruments Incorporated 50Analog Applications Journal Analog and Mixed-Signal ProductsNovember 2000Again, assuming AF\f1 1 and AF\f2 1, this reduces to(15) .)()(V2)]1)(V()1)(V[(2V2121OCM2IN1INOD\f+\f\fŠ\f+\fŠŠŠ\fŠ+= Continued from previous page R4R3++ÐÐR2R1V+OUTVÐOUTVOCMV+INAF Figure 3. Single-ended to differential amplifier ++ÐÐR2R1 V+OUTVÐOUTVOCMV+INAF Figure 4. \f1= 0 R4R3++ÐÐ V+OUTVÐOUTVOCMV+INAF With a slight variation of Figure 1 as shown in Figure 3,reducing the dynamic range of the amplifier. To stripdifferently, making V .)()(V2)1)(V(2V2121OCM1INOD\f+\f\fŠ\f+\fŠ+= ,)()1)(V(V2)V(211IN2OCMOUT\f+\f\fŠ+Š\f=Š ,)(V2)1)(V()V(211OCM1INOUT\f+\f\f+\fŠ+=+ .R1R21=\f\fŠ .A1111)A1(A)V()V()V()V(FFFININOUTOUT\b\t\n\f+×\f\fŠ=\f+=ŠŠ+ŠŠ+ Texas Instruments Incorporated 51Analog Applications Journal differential amplifier, and matching of the open-loop gainsWith = 0, this circuit is similar to a noninverting amplifier. ,V2)1)(V()V(OCM11INOUT+\f\fŠ+=+ .V2)V(2VOCM2INODŠ\f+= ,)V(V2)V(2INOCMOUT\f+Š=Š ,)V()V(2INOUT\f+=+ With = 0.333; or, with This circuit realizes a gain of 2 with no resistor. .]V)V(2[VOCMINODŠ+= ,)V(V2)V(INOCMOUT+Š=Š ),V()V(INOUT+=+ .)1()1(V2)1)(V(2V11OCM1INOD+\fŠ\f+\fŠ+= ,1)1)(V(V2)V(11INOCMOUT+\f\fŠ+Š=Š ,1V2)1)(V()V(11OCM1INOUT+\f\f+\fŠ+=+ .V2)1)(V(2VOCM11INOD+\f\fŠ+= ,)1)(V()V(11INOUT\f\fŠ+Š=Š R4R3++ÐÐV+OUTVÐOUTVOCMV+INAF Figure 6. \f2= 1 ++ÐÐV+OUTVÐOUTVOCMV+INAF Figure 7. \f1= 0, and \f2= 1Continued on next page in a similar manner, as shown below.the resistor number, k is BoltzmannÕs constant (1.38 x .R4R3R3R4REQ2+= R2R1R1R2REQ1+= Texas Instruments Incorporated 52Analog Applications Journal /2), and half is/2). Therefore,/2) and (ÐE/2) are correlated to one another andTo combine noncorrelated noise voltages, a sum-of-squaresthe square of the individual RMS voltages added together.the amplifierÕs noise sources. .)(E2E21INOD\f+\f= .)(A211E2E21F21INOD\b\b\t\n\f+\f+\b\t\n\f+\f= .2)E(2)E(EAE2OD1ODINFOD\f+Š\fŠ+= ).EA(E2E2EIDODODOD==\b\t\nŠŠ\b\t\n+ Continued from previous page VÐVIx RINEQ1Ix RINEQ2 +++ÐÐ\r Figure 9. Block diagram of the amplifierÕs R4R3R2R1EINECMER1ER3ER4ER2++ÐÐIÐINI+IN V+OUTVÐOUTVOCMAF Figure 8. Noise analysis circuit Texas Instruments Incorporated 53Analog Applications Journal Similarly, the noise contributions from Iandrespectively.differential noise voltageequal to)to a maximum absolute value of 2 (given = 0,or earlier, the differential output noise contribution isfor each resistor respectively. .EE)()]1)(E(2[)]1)(E(2[)](E2[)RI2()RI2()E2(E2R42R222121R322R1221CM2EQ2IN2EQ1IN2INOD++\f+\f\fŠ+\fŠ+\fŠ\f+×+×+= )()1)(E(2211R3\f+\f\fŠ )()1)(E(2212R1\f+\f\fŠ .)()(E22121CM\f+\f\fŠ\f ,)(R2I21EQ2IN\f+\f× )(RI221EQ1IN\f+\f× ,EEINOUT\f= resistor, the same as a standard single-ended voltage feedback amplifier. ,RR11GGFn+=\f= .2G21n\f+\f= loadan Acrobat Reader file at www-s.ti.com/sc/techlit/the materials listed below.Document TitleTI Lit. #1.Jim Karki, ÒFully differential amplifiers,Ó 2000), pp. 38-41 . . . . . . . . . . . . . . . . . . . . . . .slytRelated Web siteamplifier.ti.com IMPORTANT NOTICE Texas Instruments Incorporated and its subsidiaries (TI) reservestandard warranty. 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