EEE118: Electronic Devices and Circuits

Transcription

1 EEE118: Electronic Devices and Circuits Lecture XVII James E Green Department of Electronic Engineering University of Sheffield j.e.green@sheffield.ac.uk

2 Review Looked (again) at Feedback for signals and for DC (quiescent) conditions in a one transistor amplifier with and without emitter decoupling The situation where R L = R E is called a phase splitter. Looked at the small signal equivalent circuit of a BJT in terms of a one transistor amplifier Gave an example of a performance evaluation Noted that the value of the small signal circuit is to show which device and circuit affect the gain, not to give a numerical value (although this is possible.) Introduced the idea of an analogue building block - opamp presented the opamp as an implementation of a classical feedback system. Derived the opamp equation and presented a circuit symbol for an opamp. 2/ 22

3 Outline 1 Opamp Circuits A v : Non-Inverting A v : Inverting A v Non-Inverting A v Inverting 2 Special Case: Unity Gain Buffer 3 Circuits with Multiple Inputs Summing Amplifier Subtractor or Difference Amplifier 4 A General Multiple Input Circuit 5 Homework 5 6 Review 7 Bear 3/ 22

4 Opamp Circuits A v : Non-Inverting Opamp Circuits - Non Inverting The most common opamp circuits are the non-inverting amplifier and the inverting amplifier. It is usual to assume initially that A v. This means that the circuit behaviour is completely controlled by the feedback. If A v =, for finite then v v and this makes the calculation quite straightforward. A v v = (1) v = and v = v = (2) = (3) = (4) 4/ 22

5 Opamp Circuits A v : Inverting Opamp Circuits - Inverting In the inverting amplifier v is grounded and is applied to. If A v =, v = v and since v is connected to ground v must be very close to ground. It is often called a virtual earth. The potential is always close to zero but the node is not actually connected to zero. To obtain the gain sum currents at the v node. v i i i f = 0 (5) v = 0 (6) v = 0 so = 0 (7) i i i f vo = (8) 5/ 22

6 Opamp Circuits A v : Inverting Notice the - sign in the inverting gain formula. This means that the signal is inverted i.e. phase shifted by 180 as well as being amplified. Two inverting amplifiers in series would give rise to an overall non-inverting amplifier. The first stage would invert the signal and the second would invert it back to its original phase. i i i f R 3 R 4 6/ 22

7 Opamp Circuits A v Non-Inverting Effects of Finite Gain Occasionally it is necessary to consider the effect of finite A n the overall gain of the circuit. When considering the effects of finite gain the approximation v v does not hold. As before, using potential division at the output, A v v = (9) v = (10) But now the opamp equation must be used to relate v, v and, ( = A v v v ) ( ) = A v (11) 7/ 22

8 Opamp Circuits A v Non-Inverting [ 1 or, R ] 1 = (12) A v or, = 1 1 R (13) 1 A v 1 Note if A v, A v becomes very small and (13) becomes (4). A s equivalent to G in the classical feedback system. It is between several thousand and several hundred thousand in most opamps. A s actually frequency dependent, but the frequency dependence of A s not covered in this course. 8/ 22

9 Opamp Circuits A v Inverting For the inverting case start as before, by summing currents at the v node, i i i f vo i i i f = 0 or v which can be transposed to yield, v = 0 (14) v = (15) and v = 0 (16) Using the opamp equation = A v (0 [ ]) (17) 9/ 22

10 Opamp Circuits A v Inverting [ 1 or R ] 1 = (18) A v or = 1 A v (19) If A v, reduces to (8). Frequency dependent amplifiers (filters) can be produced by using frequency dependent passive components (inductors and, more usually, capacitors) in place of the resistors. and can become Z 1 and Z 2 and may be arbitrarily complex passive circuits. Particular arrangements of resistors and capacitors in opamp circuits can be used to produce circuits which perform mathematical functions such as integration and differentiation. 10/ 22

11 Opamp Circuits A v Inverting Input Resistance The input to the non inverting circuit goes directly to the opamp so the circuit input resistance is the same as the opamp - very large ( 10 9 ). The inverting circuit is slightly different. Taking the A v case, an input current, i i, of flows from the source. Input resistance is the ratio of the applied signal voltage to the current drawn, i.e. i i =. This is typically a few kω which makes inverting amplifiers unsuitable as amplifiers of signals derived from sources with a large thévenin resistance. 11/ 22

12 Special Case: Unity Gain Buffer Unity Gain Buffer The unity gain buffer is a special case of the non inverting amplifier, in which = 0 and =. Here v = so the opamp equation becomes, = A v ( v v ) = A v ( ) (20) Av or 1 = = A v (21) 1 1 A 1 v A v If A s large, is very close to unity. This circuit is used to isolate high impedance sources from low impedance loads; i.e. it has a high power gain. vo 12/ 22

13 Circuits with Multiple Inputs Summing Amplifier Summing Amplifier Assume A v so v virtual earth (i.e. 0 V) i1 v 2 i2 v 1 v 3 i3 R 3 v n in R n R f i f or, i f i 1 i 2 i 3 i n = 0 v 1 v 2 v 3 v n = 0 R f R 3 R n = [ ] R f R f R f R f v 1 v 2 v 3 v n R 3 R n Many audio mixers use this circuit. 13/ 22

14 Circuits with Multiple Inputs Subtractor or Difference Amplifier Subtracting Amplifier i f Several avenues of solution are available for this circuit. Assume A v = and so v = v. v 2 v 1 i i One approach is to work out v and v and then equate them to get in terms of v 1 and v 2. Summing currents at the v node, i i i f = 0 or v 2 v v = 0 (22) 14/ 22

15 Circuits with Multiple Inputs Subtractor or Difference Amplifier This can be transposed to give, v = v 2 R1 (23) v is a potentially divided version of v 1 equating v and v, v = v 1 (24) v 2 = v 1 (25) or = v 1 v 2 (26) or = (v 1 v 2 ) (27) Note that the accuracy of the subtraction depends upon matching the the two s and s. 15/ 22

16 A General Multiple Input Circuit A General Multiple Input Circuit The subtractor circuit can be generalised to allow more than two inputs. Such a circuit could be analysed by find v and v and equating them, or by using the principle of superposition. Superposition has the advantage that at each stage the circuit is reduced to a much simpler single input circuit. For example, v 1 R f v 2 v 3 R 3 R 4 v 4 16/ 22

17 A General Multiple Input Circuit Consider first the output due to v 1. v 2, v 3 and v 4 are grounded. The circuit becomes an inverting amplifier. i i R f i f vo Since both v 3 and v 4 are zero v is zero and v is a virtual earth. No current flows through so it has no effect on the circuit. ( ) Rf v1 = v 1 (28) v 1 v 2 v 3 R 3 v 4 R 4 R f 17/ 22

18 A General Multiple Input Circuit By changing the variable names the output voltage due to v 2 can be found, ( ) Rf v2 = v 2 (29) The output due to v 3 leads to a more complex circuit however. v 3 // R 3 R f Here v 1 and v 2 are grounded so is effectively in parallel with. v is a potentially divided version of v 3. So, v = R f // // (30) R 4 v 3 = R 4 R 3 R 4 (31) 18/ 22

19 A General Multiple Input Circuit By a similar argument, v 3 = v v v 3 = R 4 R 3 R 4 Rf // // (32) or v v3 = v 3 R 4 R 3 R 4 Rf // // (33) v4 = v 4 R 3 R 3 R 4 Rf // // (34) total = v 1 v 2 v 3 v 4 (35) Note: if any of the inputs have both a DC and AC component, superposition allows them to be treated separately. 19/ 22

20 Homework 5 Homework 5 It should be possible to fully attempt the Homework 5 now. It should also be possible to fully attempt the Operational Amplifiers problem sheet. 20/ 22

21 Review Review Considered circuit diagrams for a common set of opamp circuits and derived results for the output voltage due to one or more inputs: Non inverting amplifier with A v = Inverting amplifier with A v = Non inverting amplifier with A v Inverting amplifier with A v Unity gain buffer Multiple input circuits Summing Amplifier Difference Amplifier (Subtractor) General multiple input opamp circuit 21/ 22

22 Bear 22/ 22