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Modern Instrumentation PHYS 533/CHEM 620

Modern Instrumentation PHYS 533/CHEM 620. Lecture 4 Amplifiers Amin Jazaeri Fall 2007. Amplifiers. Properties of a perfect amplifier: Infinite gain Infinite input impedance will not load down source Zero output impedance will drive anything Infinite CMRR Zero Common mode voltage gain

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Modern Instrumentation PHYS 533/CHEM 620

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  1. Modern InstrumentationPHYS 533/CHEM 620 Lecture 4 Amplifiers Amin Jazaeri Fall 2007

  2. Amplifiers Properties of a perfect amplifier: • Infinite gain • Infinite input impedance • will not load down source • Zero output impedance • will drive anything • Infinite CMRR • Zero Common mode voltage gain • Infinite Bandwidth

  3. Operational Amplifiers • An operational amplifier is modeled as a voltage controlled voltage source. Properties of Op-amps • Gain ~ 106 • Input impedance ~ 100 M W • Output impedance ~ 100 W • Bandwidth ~ 1-20MHz • Common mode voltage gain ~ 10-5

  4. Amplifiers Problems • Gain too high • slightest input noise causes max output • Other problems to be discussed later Solutions • Use feedback • Gain depends only on resistance: Rf / Rin • can control precisely

  5. Applications of Op Amps • Amplifiers provide gains in voltage or current. • Op amps can convert current to voltage. • Op amps can provide a buffer between two circuits. • Op amps can be used to implement integrators and differentiators. • Lowpass and bandpass filters.

  6. + - The Op Amp Symbol High Supply Non-inverting input Output Inverting input Ground Low Supply

  7. The Op Amp Model v+ Non-inverting input + vo Rin + – Inverting input – A(v+ -v- ) v-

  8. Operational Amplifier (OP-AMP) • Basic and most common circuit building device. Ideally, • No current can enter terminals V+ or V-. Called infinite input impedance. • Vout=A(V+ - V-) with A →∞ • In a circuit V+ is forced equal to V-. This is called the virtual ground property. • An opamp needs two voltages to power it Vcc and -Vee. These are called the rails. A Vo = (A V -A V ) = A (V - V ) + - + -

  9. Offset null Not used 7 6 5 8 Offset null 1 2 3 4 Characters of Operational Amplifiers • high open loop gain • high input impedance • low output impedance • low input offset voltage • low temperature coefficient of input offset voltage • low input bias current • wide bandwidth • large common mode rejection ratio (CMRR)

  10. INPUT IMPEDANCE Input Circuit Output Input impedance: the impedance seen by the sensor when connected to the op-amp. Typically this impedance is high (ideally infinite) It varies with frequency. Typical impedances for conventional amplifiers is at least 1 M but it can be of the order of hundreds of M for FET input amplifiers. This impedance defines the current needed to drive the amplifier and hence the load it represents to the sensor. Impedance between input terminals = input impedance

  11. Impedance between output terminals = output impedance Input Circuit Output OUTPUT IMPEDANCE Output impedance: the impedance seen by the load. Ideally this should be zero since then the output voltage of the amplifier does not vary with the load In practice it is finite and depends on gain. Usually, output impedance is given for open loop whereas at lower gains the impedance is lower. A good amplifier will have an output resistance lower than 1.

  12. Vout A Non-linear region Vin Linear region Voltage output • The linear range of an amplifier is finite, and limited by the supply voltage and the characteristics of the amplifier. • If an amplifier is driven beyond the linear range (overdriven), serious errors can result if the gain is treated as a constant.

  13. Bandwidth • Bandwidth: the range of frequencies that can be amplified. • Usually the amplifier operates down to dc and has a flat response up to a maximum frequency at which output power is down by 3dB. • An ideal amplifier will have an infinite bandwidth. • The open gain bandwidth of a practical amplifier is fairly low • A more important quantity is the bandwidth at the actual gain

  14. Bandwidth

  15. Temperature & Noise • Temperature and noise refer to variations of output with temperature and noise characteristics of the device respectively. • These are provided by the data sheet for the op-amp and are usually very small. • For low signals, noise can be important while temperature drift, if unacceptable must be compensated for through external circuits.

  16. Signal Conditioning External Power + Filter Motor, Speaker, Alarm etc. Amp Transducer -

  17. Op-Amp (Analysis) • The key to op amp analysis is simple • No current can enter op amp input terminals. • => Because of infinite input impedance • The +ve and –ve (non-inverting and inverting) inputs are forced to be at the same potential. • => Because of infinite open loop gain • Use the ideal op amp property in all your analysis.

  18. What is inside an op-amp

  19. Inverting Amplifier

  20. RF iF V- i- R1 i1 i+ - Vin A V+ Vout + B R or Analysis of Inverting Amplifier Ideal transfer characteristics:

  21. Inverting op-amp • The output is inverted with respect to the input (180 out of phase). • The feedback resistor, Rf, feeds back some of this output to the input, effectively reducing the gain. • The gain of the amplifier is now given as: In the case shown here this is exactly –10

  22. Inverting op-amp • The input impedance of the amplifier is given as Here it is equal to 1 k. If a higher resistance is needed, larger resistances might be needed Or, perhaps, a different amplifier will be needed (noninverting amplifier)

  23. Inverting op-amp • The output impedance of the amplifier is given as AOL is the open loop gain as listed on the data sheet Open loop gain is the open loop gain at the frequency at which the device is operated

  24. Inverting op-amp • Example, for the LM741 amplifier, the open loop output impedance is 75W and the open loop gain at 1 kHz is 1000. This gives an output impedance of: The bandwidth is also influenced by the feedback:

  25. Non-Inverting Amplifier

  26. Non-inverting amplifier • The non-inverting amplifier gain is: For the circuit shown, this is 11 The gain is slightly larger than for the noninverting amplifier for the same values of R. The main difference however is in input impedance.

  27. Non-inverting amplifier • Input impedance is: • Rop is the input impedance of the op-amp as given in the spec sheet • Aol is the open loop gain of the amplifier. • Assuming an open loop impedance of 1 M (modest value) and an open loop gain of 106, we get an input impedance of 1011. (almost ideal)

  28. Non-inverting amplifier • The output impedance and bandwidth are the same as for the inverting amplifier. • The main reason to use a noninverting amplifier is that its input impedance is very large making it almost ideal for many sensors. • There are other properties that need to be considered for proper design such as output current and load resistance but these will be omitted here for the sake of brevity.

  29. The voltage follower

  30. Voltage follower The input impedance now is very large and equal to: The output impedance is very small and equal to:

  31. Voltage follower • The value of the voltage follower is to serve in impedance matching. • One can use this circuit to connect, say, a capacitive sensor or, an electronic microphone. • If amplification is necessary, the voltage follower may be followed by an inverting or noninverting amplifier

  32. - + Non-ideal op-amp Rf R1 Vin1 Vout R2 Vin2 ~ R3 Differential Amplifier • Op amp output actually depends on voltage difference at two inputs • Insensitivity to common voltage at both inputs = CMRR • Real op amps have problems with unbalanced input impedance

  33. Differential Amplifier Redefine the inputs in terms of two other voltages: 1. differential mode inputvdmvb– va 2. common mode inputvcm (va+ vb)/2 so that va = vcm – (vdm/2) and vb = vcm + (vdm/2) Then it can be shown that “common mode gain” “differential mode gain”

  34. Differential Amplifier • An ideal differential amplifier amplifies only the differential mode portion of the input voltage, and eliminates the common mode portion. • provides immunity to noise (common to both inputs) • If the resistors are not perfectly matched, the common mode rejection ratio (CMRR) is finite:

  35. SUMMING AMPLIFIER Recall inverting amplifier and If = I1 + I2 + … + In If VOUT = -Rf (V1/R1 + V2/R2 + … + Vn/Rn) If R1=R2=…=Rf, then Vout = V1 + V2 +…+Vn Summing amplifier is a good example of analog circuits serving as analog computing amplifiers (analog computers)! Note: analog circuits can add, subtract, multiply/divide (using logarithmic components, differentiat and integrate – in real time and continuously.

  36. Frequency Response

  37. Circuit building Tips +Vcc=+15V Signal 1) Pin numbers on the circuit diagram R2 R1 Eg. R2 2 7 R1 - 3 8 7 6 5 6 + 4 To Oscilloscope 741 Gnd 2) Use color coding 1 2 3 4 3) Use power strips 4) Separate components from chip - use insulated wire back to chip 5) Scope probes - to scope (ground) BNC cable - from signal generator 6) Build and check in sections -Vcc=-15V GND

  38. Trouble Shooting Tips Bread board wiring Check circuit diagram Check breadboard wiring Check supply voltages Check voltages at nodes of Interest in your circuit To oscilloscope 8 7 6 5 2 7 - 741 3 6 + 4 1 2 3 4 To signal generator Circuit diagram Write down pin numbers on the circuit diagram Use different color wires for supply and signals

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