Study of a Difference Amplifier - Circuit Analysis I - Lab | EGR 214, Lab Reports of Electrical Circuit Analysis

Download Study of a Difference Amplifier - Circuit Analysis I - Lab | EGR 214 and more Lab Reports Electrical Circuit Analysis in PDF only on Docsity! Study of a Difference Amplifier by Dan VanderBoon EGR 214 Circuit Analysis I Instructor: Dr. Rahman Lab Section: 5 Grand Valley State University Padnos College of Engineering & Computing School of Engineering April 7, 2005 1 Abstract – This report presents the study of a difference amplifier circuit. The difference amplifier circuit was analyzed, simulated, built, and tested. The differential mode gain (Adm), common mode gain (Acm), and common mode rejection ratio (CMRR) were calculated and measured. CMRR is used to measure how nearly ideal a difference amplifier is. The CMRR for the circuit analyzed in this study was calculated as 528.5 and measured as 543.81. The percent error between these values was 2.897%. I. INTRODUCTION Circuit analysis is a critical part of understanding and developing modern circuits. The leading linear active device in modern circuits is the integrated circuit operational amplifier. Operational amplifiers were first mentioned in a 1947 paper by John R. Ragazzini and his colleagues [1]. The paper described high-gain dc amplifier circuits carrying out mathematical operations, hence the term operational amplifier [1]. The particular operational amplifier circuit analyzed in this study is the difference amplifier or subtractor. Its output voltage is proportional to the difference of the two input signals. Difference amplifiers are common in many circuits. One of their applications is the solenoid and motor control circuits found in automotive systems. The difference amplifier is especially valuable because of its ability to differentially take signals from lines or sensors subject to common mode voltages [2]. In other words, the difference amplifier cancels the signal common to both inputs. The difference amplifier enables easy connection to non-inverting and inverting circuits as well as output biasing [2]. The performance or idealness of a difference amplifier is typically measured by common mode rejection ratio (CMRR). Resistor matching and tight resistor tolerances are extremely important in increasing the CMRR of a difference amplifier circuit [3]. The purpose of this study is to determine how ideal a particular difference amplifier circuit is. 4 The superposition principle may be used to find VO. 02010 VVV += (7) First, V2 is supressed as shown in Figure 3. Fig. 3: Circuit with V2 supressed Because the input current to the OP AMP is zero, Kirchoff’s Current Law may be applied at the negative OP AMP node to obtain, 21 ii = . (8) The other input node of the OP AMP is connected directly to ground so the positive OP AMP node has zero voltage. Mathematically, 03 =V . (9) From Ohm’s law we can use (8) to write, 2 01 1 10 R V R V = − . (10) Rewriting (10), 22 kΩ R1 1 kΩ 1 kΩ 23 kΩ V1 R2 R3 R4 V0 i1 i2 0 A 0 A i4 i3 V3 V3 5 1 1 2 01 V R R V −= (11) Next, V1 is suppressed (Figure 4) to find V02. Fig. 4: Circuit with V1 suppressed Because the input current to the OP AMP is zero, Kirchoff’s Current Law may be applied at the positive OP AMP input node to obtain, 43 ii = . (12) From Ohm’s law we can use (12) to write, 4 3 3 12 0 R V R VV − = − . (13) Rewriting (13), 3 3 4 3 3 2 R V R V R V += . (14) Factoring out V3, 3 343 2 11 V RRR V       += . (15) V2 22 kΩ R1 1 kΩ 1 kΩ 23 kΩ R2 R3 R4 V0 i1 i2 0 A 0 A i4 i3 V3 V3 6 Rewriting (15), 3 43 43 3 2 V RR RR R V       + = . (16) Canceling out R3, 3 4 43 2 V R RR V       + = . (17) Rewriting (17), 2 43 4 3 V RR R V       + = (18) Because the input current to the OP AMP is zero assuming the ideal OP AMP model, Kirchoff’s Current Law may be applied at the negative OP AMP input node to obtain, 21 ii = . (19) From Ohm’s law we can use (21) to write, 2 302 1 3 0 R VV R V − = − . (20) Rewriting (20), 2 02 2 3 1 3 R V R V R V =+ . (21) Factoring out V3,       += 21 3 2 02 11 RR V R V . (22) Rewriting (22), 3 21 21 2 02 V RR RR R V       + = . (23) Canceling out R2, 9 )( 431 3241 RRR RRRR Acm + − = (37) and, )(2 )()( 431 432214 RRR RRRRRR Adm + +++ = . (38) We are given: Ω= Ω= Ω= Ω= K 22 K 1 K 23 K 1 4 3 2 1 R R R R Notice that 42 RR ≠ , which results in a loss of idealness or performance in the differential amplifier circuit. Substituting the resistor values into (38) we obtain, 9783.22 )221)(1(2 )221(23)231(22 = + +++ =dmA Substituting the resistor values into (37) we obtain, 04348.0 )221(1 )1(23)22(1 −= + − =cmA The Common Mode Rejection Ratio in (4) gives, 5.528 04348.0 9783.22 = − == cm dm A A CMRR IV. PSPICE SIMULATION OF 3 DIFFERENTIAL AMPLIFIER CIRCUITS P-spice is a useful tool to find the differential mode gain, common mode gain, the CMRR, and the output voltage. The P-spice circuits are shown in Appendix A; the results are shown in Table 1. 10 TABLE 1: PSPICE VOLTAGES Circuit 1 Circuit 2 Circuit 3 V1 -0.25 V 5 V 5 V V2 0.25 V 5 V 5.5 V V0 11.49 V -0.22045 V 11.26 V A. Circuit 1 To find the differential mode gain (Adm) we let vcm = 0. On this condition (1) gives, dmdmO VAV = (vcm = 0) (39) If vcm = 0, then (3) gives, 21 21 0 2 VV VV Vcm −= = + = (40) Let V1 = -0.25 V and V2 = 0.25 V. From (39) and (2) we can say that, 98.22 25.025.0 49.11 = + == dm O dm V V A (41) B. Circuit 2 To find the common mode gain (Acm) we let vdm = 0. On this condition (1) gives, cmcmO VAV = (vdm = 0) (42) If vdm = 0, then (2) gives, 21 12 0 VV VVVdm = =−= (43) Let 521 ==VV V. From (42) and (3) we can say that, 04409.0 2)55( 22045.0 −= + − == cm O cm V V A (44) The CMRR of the circuit can be calculated from (41), (44), and (4). 11 2.521 04409.0 98.22 = − == cm dm A A CMRR (45) C. Circuit 3 Let 51 =V V and =2V 5.5 V. From (29) we get the same value obtained in P-spice, 26.115 1 23 5.5 22 1 1 23 1 1 1 23 1 1 1 1 2 2 4 3 2 1 1 2 0 =−             + + =−             + + = V R R V R R R R R R V V TABLE 2: PSPICE RESULTS Circuit Value Adm 1 22.98 Acm 2 -0.04409 CMRR 1,2, & 3 521.2 V0 3 11.26 V V. EXPERIMENT A. Experimental Equipment The following equipment was used: • 1 TENMA Universal Test Center • 1 breadboard • Miscellaneous wires • 5 resistors (1 kΩ, 1kΩ, 1 kΩ, 22 kΩ, 22 kΩ) • 1 uA741 OP AMP B. Experimental Results Using the equipment the circuit was built and tested. Table 3 shows the experimental results. 14 22 1 23 1 = . This shows why the CMRR was only calculated as 528.5. If 42 RR = , the differential amplifier that was studied would have been much more ideal. VII. CONCLUSIONS This report presented the study of a difference amplifier circuit. The purpose of the report was to determine the performance of a particular differential amplifier circuit using CMRR. The CMRR was calculated after analyzing the circuit. Two circuits simulated on P-spice found the common mode gain and the differential mode gain. The ratio of the gains was similar to the calculated CMRR value. Finally, 3 circuits were built and tested to verify the CMRR that was calculated and to test the performance of the difference amplifier model. The measured CMRR was 544 which showed that the difference amplifier was nearly ideal. The % error between the measured CMRR and the simulated CMRR was 4.3%. The % error between the measured CMRR and the calculated CMRR was 2.9%. These errors were thought to have come from unaccounted resistance present in the OP AMP and wires, varying voltage supplies, and poor resistor tolerances. The reason that the circuit is not more ideal is because 42 RR ≠ . REFERENCES [1] R. E. Thomas and A. J. Rosa, The Analysis and Design of Linear Circuits: Laplace Early. 4 th edition. Hoboken, NJ: John Wiley & Sons, 2004, ch. 4. [2] Jerry Steele, “What’s Different about Difference Amplifiers?” Senior Technical Staff, Burr- Brown Division, Texas Instruments Incorporated. [3] Giampaolo Marino, Soufi ane Bendaoud, and Steve Ranta, “Universal Precision Op Amp Evaluation Board.” AN-692 Application Note. Analog Devices, Norward, MA 15 APPENDIX A Fig. 5: Circuit 1 - used to find Differential Mode Gain Fig. 6: Circuit 2 - used to find Common Mode Gain 16 Fig. 7: Circuit 3 - used to test performance of the difference amplifier