Lecture 3: Opamp Review. Basic Opamp

Transcription

1 Lecture 3: Opamp eview Invertg amplifier Generalized impedances Invertg tegrator Invertg differentiator Weighted summer Non-vertg amplifier oltage buffer Non-lear amplifiers First, assume ideal op amp. Basic Opamp Op amp is a circuit that has two puts and one put. It amplifies the difference between the two puts.

2 Note: Negative feedback Fd close loop ga Analysis Invertg Amplifier irtual short circuit: Due to fite ga of op amp, the circuit forces 2 to be close to, thus creatg a virtual short. Closed loop ga 0 i 2 Invertg Amplifier Note that the virtual ground is not actually shorted to ground; otherwise this would force all the current flowg through 2 to ground and would be zero. The behavior of the virtual ground is similar to a seesaw, where the pot between the two arms is pned (does not move), allowg the displacement at pot A to be amplified (and verted ) at pot B. 2

3 Non-vertg amplifier A nonvertg amplifier returns a fraction of put signal thru a resistor divider to the negative put. With a high Ao, / depends only on ratio of resistors, which is very precise Closed loop ga Extreme Cases of 2 (Infite A 0 ) If 2 is zero, the loop is open and / is equal to the trsic ga of the op amp. If 2 is fite, the circuit becomes a unity-ga amplifier and / becomes equal to one. 3

4 Unity Ga Amplifier Why use this if =? Another iew of Invertg Amplifier For large /2, magnitude of closed loop ga is roughly the same. Why use one over the other? Invertg Nonvertg In contrast with the non-vertg amplifier, the vertg amplifier exhibits an put resistance of 2. Decreasg 2 creases the closed loop ga but also decreases the put resistance. 4

5 oltage Adder or Weighted Summer Complex Impedances Around the Op Amp Z Z 2 eplace and 2 with impedances, Z and Z 2. The closed-loop ga is still equal to the ratio of two impedances. Transfer function: Magnitude Phase 5

6 Example: Invertg Integrator Z 2 = Z = /sc Time Doma ( t) i( t) qc ( t) vc( t) C C ( t) v o c q ( t) C ( t) C C i ( t) dt i ( t) dt i( t) dt C dt ( t) dt C s ( jω) ( jω) jω C ( jω) 90 ( jω) Frequency Doma ( s) ( s) C s ( jω) ωt ( jω) ω C ω C s ω t C Example: Invertg Integrator Z 2 = Z = /sc ω t C Is the tegrator frequency Frequency Doma Note that at ω=0, the impedance of C is fite and the opamp operates open loop (i.e. no negative feedback). That is, the ga at DC is fite, as the open loop ga is fite. This should also be obvious from the transfer function: C s where the root of the denomator, or pole of the transfer function, is at zero (i.e. DC). In practice, sce at DC the opamp is open loop configuration, any DC offsets will saturate the put. How do you fix this? 6

7 Integrator with Pulse Input dt t 0t Tb C C Comparison of Integrator and C Lowpass Filter The C low-pass filter is actually a passive approximation to an tegrator. With the C time constant large enough, the C filter put approaches a ramp. 7

8 Lossy Integrator Consider the case when Ao is fite X X C s X Ao X Ao C s A0 A0 When fite op amp ga is considered, the tegrator becomes lossy as the pole moves from the orig to -/[(+A 0 )C]. It can be approximated as an C circuit with C boosted by a factor of A 0 + Note: pole frequencies are obtaed by settg he denomator of the transfer function to zero Differentiator d C dt C s C s 8

9 Differentiator with Pulse Input C ( t) Comparison of Differentiator and High-Pass Filter The C high-pass filter is actually a passive approximation to the differentiator. When the C time constant is small enough, the C filter approximates a differentiator. 9

10 Lossy Differentiator Consider the case when Ao is fite X X Cs X Ao X A C s Cs o A A 0 0 When fite op amp ga is considered, the differentiator becomes lossy as the zero moves from the orig to (A 0 +)/C. It can be approximated as an C circuit with reduced by a factor of (A 0 +). Precision ectifier Suppose we want to elimate the diode voltage drop (i.e. dead zone) associated with a simple rectifier circuit. Assume a unity-ga buffer tied to the resistive load. High ga of opamp ensures X tracks. Insert a diode to break connection and hold X at zero durg negative cycles. Assume =0; the opamp raises y to don to hold X at roughly zero. If becomes positive, X tracks. If becomes negative, y goes negative. Sce D cannot carry current (reversed biased), the opamp produces a very large negative put (near the negative rail). 0

11 Invertg Precision ectifier When is positive, the diode is on, y is pned around D,on, and x at virtual ground. When is negative, the diode is off, y goes extremely negative, and x becomes equal to. Logarithmic Amplifier T ln I S By sertg a bipolar transistor the loop, an amplifier with logarithmic characteristic can be constructed. This is because the current to voltage conversion of a bipolar transistor is a natural logarithm. Logamps are useful applications where the put signal may vary by a large factor. In such cases, weak signals are amplified and strong signals are attenuated (compressed), hence the log dependence. Logamps implement the verse function of the exponential characteristic

12 Square-oot Amplifier 2 W nc ox L TH By replacg the bipolar transistor with a MOSFET, an amplifier with a squareroot characteristic can be built. This is because the current to voltage conversion of a MOSFET is square-root. Similar to the logamp usg a bipolar transistor the feedback path, the square root amp implements the verse function of the MOS quadratic current dependence on GS 2