Operational Amplifiers

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1 Operational Amplifiers Aims: To know: Basic Op Amp properties eal & Ideal Basic ideas of feedback. inv input noninv input output gnd To be able to do basic circuit analysis of op amps: using KCL, KL with dependent sources. Inverting and Noninverting Amplifiers. oltage follower and summing amplifier. Lecture 7 1 oltage Amplifiers Probably the most common building block in electronics is the voltage amplifier. Often shown schematically as A A out db = A in out = 0 log 10 in The key requirement is the ability to generate an exact copy of an input waveform without modifying its shape or time dependence. Key parameters are: Linearity Well controlled frequency response High input impedance Low output impedance Lecture 7 1

2 Linearity Ideal linear characteristic (slope = gain) eal characteristic (exaggerated) saturation out distortion zero offset in Lecture 7 3 Frequency esponse eal characteristic (exaggerated) Peaking Ideal characteristic Gain (db) Low frequency rolloff High frequency rolloff ω Lecture 7 4

3 Input and Output Impedance (esistance) Thevenin equivalent of source Z T Z Amplifier A Z Load L Z L T (Two port equivalent circuit) Input impedance: Must be high to ensure that is a good approximation to T Z = T Z Z T Output impedance: For voltage amplifier Z must be low to ensure that L is a good approximation to =A For power amplifier = L, or more generally for impedances Z =Z * L (maximum power transfer) Lecture 7 5 The Operational Amplifier This is an important building block that allows us to construct amplifiers with a wide range of characteristics. out inv input noninv input in Controlled voltage source = A( ) output The key features are TWO inputs: Inverting and Noninverting ( and ) Output is a controlled voltage source with a value A( ). A is very large ery high input resistance ( in ) ery low output resistance ( out ) Lecture 7 6 3

4 Op Amps Package outline Detailed schematic All components fabricated on a small chip of silicon (< 1 mm square) inv input noninv input output gnd Circuit symbol Lecture 7 7 Op Amp Parameters Parameter Ideal op amp eal op amp inv input noninv input output gnd Open loop gain, A Input resistance in Output resistance MΩ 1 GΩ Ω Three important consequences: 1) ery small (or zero) currents flow into the input terminals ) Output is like an ideal voltage source ( out independent of current) 3) oltage difference between input terminals is very small (or zero) because of large gain out = A ( ) ( ) = / A, which 0 as A out Lecture 7 8 4

5 Feedback Amplifier (inverting amplifier) 1 1 rin X I 1 I r out schematic equivalent circuit Generally two ways of analysing these circuits: (i) Assume OpAmp is ideal (ii) Assume Open loop gain, A, is finite initially. Lecture 7 9 Feedback Amplifier (inverting amplifier) 1 1 rin X I 1 I r out schematic equivalent circuit For an ideal opamp, no current flows into _, so I 1 = I (KCL) For an ideal opamp, open loop gain is infinite, so _ = = 0 Point X is a virtual earth. Earth because = 0, virtual because there is a high impedance to true earth I = = I = 1 1 =

6 Feedback Amplifier (inverting amplifier) 1 1 rin X I 1 I r out schematic equivalent circuit For an ideal opamp, no current flows into _, so I 1 = I (KCL) For an ideal opamp, open loop gain is infinite, so _ = = 0 Point X is a virtual earth. Earth because = 0, virtual because there is a high impedance to true earth I = = I = 1 1 = Feedback Amplifier (inverting) 1 X = 1 Closed loop gain This is a remarkable result this tells us that for an ideal amplifier, the gain is determined ONLY by the feedback components and not by the properties of the amplifier. This is negative feedback. ery important in the design of many kinds of amplifier. You can think of this as a kind of thermostat trying to keep equal to. If _ rises, then falls and corrects _ by exactly the right amount. Lecture

7 Feedback Amplifier (noninverting) 1 Now is equal to the input voltage (no current into the terminal so = independently of ) Open loop gain is, so = =, so Lecture 7 15 Feedback Amplifier (noninverting) 1 Now is equal to the input voltage (no current into the terminal so = independently of ) Open loop gain is, so = =, so so = = (potential divider) Lecture

8 oltage Follower A special case of the noninverting amplifier with 1 = and =0 so = The output voltage is an exact copy of the input. Because the input impedance is very high, this circuit is very useful for separating (buffering) two parts of a circuit (e.g. sections of a filter) Lecture 7 18 Summing Amplifier F The current balance at the virtual earth now gives us 1 3 = 1 3 F 1 3 = F K If all resistors are equal, the output voltage is the sum of the input voltages (negative) Lecture

9 Active Filters Opamps can simplify filter design by giving a high impedance separation between different C or L sections of a circuit and by offering gain to compensate for the loss in the passive filter: E.g. bandpass filter: C This circuit has a transfer function like 0 A (db) Note the gain is > 1 C Using an op amp allows complex filters to be constructed. log 10 ω Lecture 7 1 9

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