INTRODUCTION TO MECHATRONICS: OPERATIONAL AMPLIFICATORS Introduction to mechatronics

ME 6405 Introduction to Mechatronics Contents Introduction Theory A. Definition and presentation B. Linear Mode C. Non Linear Mode Real Operational Amplificators Uses Conclusion References ME 6405 Introduction to Mechatronics

Definition and presentation Operational Amplifier (Op Amp) Definition: a high gain electronic amplifying circuit element in a feedback amplifier, that accomplishes many functions or mathematical “operations” in analog circuits. Theory ME 6405 Introduction to Mechatronics

Definition and presentation Op Amp components: transistors resistors diodes capacitors Theory ME 6405 Introduction to Mechatronics

Definition and presentation Op Amp Circuit Model Theory ME 6405 Introduction to Mechatronics

ME 6405 Introduction to Mechatronics Op Amp Circuit Chip ME 6405 Introduction to Mechatronics

Definition and presentation Behavior assumptions for Op Amp circuit analysis : Amplifier operates in its linear amplifying region Large voltage gain (A) Theory ME 6405 Introduction to Mechatronics

ME 6405 Introduction to Mechatronics Difference between input voltages to Op Amp is very small because voltage gain (A) is very large Input impedance (Ri) is large ME 6405 Introduction to Mechatronics

ME 6405 Introduction to Mechatronics Transfer Characteristic: Modes + saturation ( ) - saturation ( ) linear ( ) ME 6405 Introduction to Mechatronics

ME 6405 Introduction to Mechatronics Op Amp transfer characteristic relation ME 6405 Introduction to Mechatronics

ME 6405 Introduction to Mechatronics Inverting Op Amp Analysis We assume that the Op-Amp gain is very high, effectively infinity. It is assumed that the amplifier operates in its linear amplifying region. ( for e.g. -10V < eo < 10V ) i2 e0 i1 ei ME 6405 Introduction to Mechatronics

ME 6405 Introduction to Mechatronics Inverting Op Amp Analysis The difference between input voltages to the op amp is very small, essentially 0. The input impedance to the op-amp is extremely large. i2 e0 i1 e' ei e+ ME 6405 Introduction to Mechatronics

ME 6405 Introduction to Mechatronics Inverting Op Amp Analysis For e.g. if |eo | < 10V and K = 105 then |e+ - e’| =10/105 = 100 V For the inverting amplifier, e+ is grounded. Hence e+ 0 and e’ 0 i2 e0 i1 e' ei e+ ME 6405 Introduction to Mechatronics

Inverting Op Amp e0 ei i2 i1 e+ e' The equation for this circuit can be obtained as follows: ME 6405 Introduction to Mechatronics

Inverting Op Amp e0 ei Since K (0 - e’) = e0 and K >>>1, then e’ 0 since ME 6405 Introduction to Mechatronics

ME 6405 Introduction to Mechatronics Inverting Op Amp i2 e0 i1 e' ei e+ Hence we have or Notice that the sign of the output voltage, e0 is the negative of that of the input voltage, ei. ME 6405 Introduction to Mechatronics

Non - Inverting Op Amp ei e0 (GROUND) For the non-inverting amplifier the input is connected to the non-inverting input. The same assumptions have been made as in the case of the Inverting Op Amp ME 6405 Introduction to Mechatronics

Non - Inverting Op Amp ei e0 For this circuit we have , (GROUND) For this circuit we have , where K is the differential gain of the amplifier. ME 6405 Introduction to Mechatronics

Non - Inverting Op Amp ei e0 This leads to (GROUND) This leads to A particular form of this amplifier is when the feedback loop is a short circuit, I.e. R2 = 0. Then the voltage gain is 1, such an amplifier is called a Voltage Follower. ME 6405 Introduction to Mechatronics

Summing Amplifier An inverting amplifier can accept two or more inputs and produce a weighted sum At X, I = IA + IB + IC and we can see that: ME 6405 Introduction to Mechatronics

Summing Amplifier By utilizing the usual assumptions, we obtain: ME 6405 Introduction to Mechatronics

Differencing Amplifier A differential amplifier is one that amplifies the difference between two voltages ME 6405 Introduction to Mechatronics

Differencing Amplifier The current through the feedback resistance must be equal to that from V1 through R1 ME 6405 Introduction to Mechatronics

Differencing Amplifier Hence which can be rearranged to give, ME 6405 Introduction to Mechatronics

Integrating Amplifier Vout Vin x Potential Difference across capacitor = VX - Vout q = CV ME 6405 Introduction to Mechatronics

Integrating Amplifier Vout Vin x Rearranging this gives Integrating both sides gives ME 6405 Introduction to Mechatronics

ME 6405 Introduction to Mechatronics Non Linear Mode General use of op amp: input output Vs1 Vs2 Theory ME 6405 Introduction to Mechatronics

ME 6405 Introduction to Mechatronics Non Linear Mode The op amp is only used in saturation mode: input output Vs1 Vs2 Theory ME 6405 Introduction to Mechatronics

Non Linear Mode Theory How to find the output: + - Vs1 If U1 > U2, U3 = Vs1 If U2 > U1, U3 = Vs2 Theory In each case, i3 is unknown and i1 and i2 are null. ME 6405 Introduction to Mechatronics

ME 6405 Introduction to Mechatronics Non Linear Mode Gate operator: OR If U1 or/and U2 = 5V, U3 = 5V If U2 and U1 = 0V, U3 = 0V 1V + - U1 U2 U3 5V 0V Theory ME 6405 Introduction to Mechatronics

ME 6405 Introduction to Mechatronics Non Linear Mode Other gate: NON OR + - U3 5V 0V 1V U1 U2 If U1 or/and U2 = 5V, U3 = 0V If U2 and U1 = 0V, U3 = 5V Theory ME 6405 Introduction to Mechatronics

ME 6405 Introduction to Mechatronics Non Linear Mode Two offsets comparator: + - U1 U2 U3 5V 0V R1 R2 If U3 = 0V U3 = 5V Theory ME 6405 Introduction to Mechatronics

ME 6405 Introduction to Mechatronics Non Linear Mode Two offsets comparator (cont): input output Vs1 Vs2 Uup Udown If U2 ≤ Udown , U3 = 0V If U2 ≥ Uup, U3 = 5V Theory ME 6405 Introduction to Mechatronics

ME 6405 Introduction to Mechatronics Non Linear Mode The square wave supplier or clock: + - U3 5V -5V R1 C R2 0V U3 will alternativelly be equal to 5V for T second and to -5V for T seconds. In this case Theory ME 6405 Introduction to Mechatronics

ME 6405 Introduction to Mechatronics Non Linear Mode The square wave supplier or clock (cont): T output time Theory ME 6405 Introduction to Mechatronics

Internal electrical schema Differential Part Gain Part Real Operational Amplificators Push/Pull Output ME 6405 Introduction to Mechatronics

Input Characteristics Input Impedance: 1M to more than 20 M and not infinite Input Offset (most important default): when V+ or V- are low or G is high  some 10 V because T1 and T2 are not exactly the same Real Operational Amplificators ME 6405 Introduction to Mechatronics

Input Characteristics Polarization currents: to polarize T1 and T2 Offset currents 1/20th to 1/5th of I+ and I- due to resistors and polarization currents Limited Input Voltage Real Operational Amplificators ME 6405 Introduction to Mechatronics

Transfer Characteristics The output is proportional to the input: It is limited by Vsat+ and Vsat- Real Operational Amplificators ME 6405 Introduction to Mechatronics

Output Characteristics Output Impedance not null:  around 100  Slew rate  0,5V/µs up to 150V/µs capacitor needs to be charged Real Operational Amplificators ME 6405 Introduction to Mechatronics

Output Characteristics Vs limited by Vsat+ and Vsat- Output currents limited (some mA) to protect op-amps  high impedances needed High Power user  250mW to several Watts Real Operational Amplificators ME 6405 Introduction to Mechatronics

ME 6405 Introduction to Mechatronics Summary Static Equivalent schema Real Operational Amplificators Dynamic Equivalent schema ME 6405 Introduction to Mechatronics

ME 6405 Introduction to Mechatronics Summary Characteristics Ideal Real Input Impedance Ze  1M up to 20 M  Output Impedance Zs 0  Some 10th  Gain 20.104 up to 20.1012 Offset 0V 25 µV up to 15 mV Real Operational Amplificators ME 6405 Introduction to Mechatronics

ME 6405 Introduction to Mechatronics Summary Characteristics Ideal Real Polarization Current 0 mA 20 pA up to 500 pA Offset Current 10 pA up to 200 mA Slow rate  V/µS 0,5 V/µS up to 100 V/µS Real Operational Amplificators ME 6405 Introduction to Mechatronics

ME 6405 Introduction to Mechatronics Solutions Be careful because Vsat+ and Vsat- are different  trigger… Be careful with high frequency integrators  Input Impedance may be too low Offset can be compensated (already exists or special schema) Real Operational Amplificators ME 6405 Introduction to Mechatronics

ME 6405 Introduction to Mechatronics Solutions Need to have same polarization currents Need to use low resistors at input to limit offset current Do not overpass Vin maxi Chose fast op-amps (10V/µs) for high frequency requirements or use a differencing comparator Real Operational Amplificators ME 6405 Introduction to Mechatronics

Practical Applications Perform math operations inexpensive and lead to easy designs that are easy to construct Power Source PID Control Filter Uses ME 6405 Introduction to Mechatronics

Characteristics / Numbers Op Amp Examples: Uses ME 6405 Introduction to Mechatronics

ME 6405 Introduction to Mechatronics CONCLUSION Introduction Theory of Op Amp’s Definition and Analysis Linear Mode Non Linear Mode Real Operational Amplifiers Uses In practice, do not hesitate to make the assemblies more abracadabrants  Have Fun ME 6405 Introduction to Mechatronics

ME 6405 Introduction to Mechatronics REFERENCES Cogdell, J.R. Foundations of Electrical Engineering. Pg 489-506, 1996 Thomas, Ronald E. The Analysis and Design of Linear Circuits. pg 186-221, 1998 Walter G. Jung, IC Op-Amp Cook Book Michel Girard, Amplificateurs opérationnels 1 & 2 www.uoguelph.ca/~antoon/gadgets/T41.htm www.national.com/appinfo/amps/ http://c3iwww.epfl.ch/teaching/physiciens/lecon07/ lecon7.html http://courelectr.free.fr/AOP/AOP.HTM ME 6405 Introduction to Mechatronics