2.6 Large Signal Operation

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1 3/4/2011 section 2_6 Large signal operation 1/2 2.6 Large Signal Operation Readg Assignment: Recall that real amplifiers are only approximately lear! If the put signal becomes too large, and/or the put signal changes too quickly, we beg to see some very non-lear behavior. Non-lear behavior leads to a distorted ouput. In other words, the output does not look like a copy of the put! The put signal cannot be too big: (A grotesque example of distortion) HO: OUTPUT VOLTAGE SATURATION The put signal cannot change too fast: HO:SLEW RATE The put signal certaly cannot be too be and change too fast! HO: FULL POWER BANDWIDTH

2 3/4/2011 section 2_6 Large signal operation 2/2

3 3/4/2011 Output voltage saturation lecture 1/9 Output Voltage Saturation Recall that the ideal transfer function implies that the output voltage of an amplifier can be very large, provided that the ga A vo and the put voltage v are large. v out A vo < 0 A vo > 0 v

4 3/4/2011 Output voltage saturation lecture 2/9 The output voltage is limited However, we found that a real amplifier, there are limits on how large the output voltage can become. The transfer function of an amplifier is more accurately expressed as: L v ( t) > L + + v ( t) = A v ( t) L v ( t) L out < < vo + L v ( t) < L

5 3/4/2011 Output voltage saturation lecture 3/9 This expression is shown graphically as: A non-lear behavior! This expression (and graph) shows that electronic amplifiers have a maximum and mimum output voltage (L + and L - ). L + v out If the put voltage is either too large or too small (too negative), then the amplifier output voltage will be equal to either L + or L -. If v out = L + or v out =L -, we say the amplifier is saturation (or compression). = L L A vo A vo L - + = L L A + vo v

6 3/4/2011 Output voltage saturation lecture 4/9 Make sure the put isn t too large! Amplifier saturation occurs when the put voltage is greater than: v L+ > L A vo + or when the put voltage is less than: v L < L A vo Often, we fd that these voltage limits are symmetric, i.e.: L = L and L = L + + For example, the output limits of an amplifier might be L + = 15 V and L - = -15 V. However, we fd that these limits are also often asymmetric (e.g., L + = +15 V and L - = +5 V).

7 3/4/2011 Output voltage saturation lecture 5/9 Saturation: Who really cares? Q: Why do we care if an amplifier saturates? Does it cause any problems, or otherwise result performance degradation?? A: Absolutely! If an amplifier saturates even momentarily the unavoidable result will be a distorted output signal.

8 3/4/2011 Output voltage saturation lecture 6/9 A distortion free example For example, consider a case where the put to an amplifier is a triangle wave: L + v (t) t L Sce L < v ( t) < L for all time t, the output signal will be with the limits L + + and L - for all time t, and thus the amplifier output will be v out (t) = A vo v (t): v out (t) L + t L

9 3/4/2011 Output voltage saturation lecture 7/9 The put is too darn big! Consider now the case where the put signal is much larger, such that v ( t) > L and v ( t) < L for some time t (e.g., the put triangle wave exceeds + the voltage limits L + and L some of the time): v (t) L + t L This is precisely the situation about which I earlier expressed caution. We now must experience the palpable agony of signal distortion!

10 3/4/2011 Output voltage saturation lecture 8/9 Palpable agony v out (t) L + t L Note that this output signal is not a triangle wave! For time t where v ( t) > L and v ( t) < L, the value A v ( t ) is greater than L + vo + and less than L -, respectively. Thus, the output voltage is limited to v ( t) = L and v ( t) = L for these times. out + out As a result, we fd that output v ( t ) does not equal A v ( t ) the output out vo signal is distorted!

11 3/4/2011 Output voltage saturation lecture 9/9 Amplifiers with op-amps For amplifiers constructed with op-amps, the voltage limits L + and L - are determed by the DC Sources V + and V - : L V + and L V + R 1 R 2 V + - ideal v out v + V

12 3/4/2011 Slew Rate lecture 1/7 Slew Rate We know that the output voltage of an amplifier circuit is limited, i.e.: L < v ( t ) < L out + Durg any period of time when the output tries to exceed these limits, the output will saturate, and the signal will be distorted! E.G.: v (t) L + t L v out (t) L + t L

13 3/4/2011 Slew Rate lecture 2/7 Limits on the time derivative But, this is not the only way which the output signal is limited, nor is saturation the only way it can be distorted! A very important op-amp parameter is the slew rate (S.R.). Whereas L - and L + set limits on the values of output signal v out (t), the slew rate sets a limit on its time derivative!!!! I.E.: dv ( t) out S.R. < < + S.R. dt In other words, the output signal can only change so fast! Any attempt to exceed this fundamental op-amp limit will result slew-rate limitg.

14 3/4/2011 Slew Rate lecture 3/7 So, addition to saturation: The red means distortion L+ if Avo v( t) > L+ vout( t) = Avo v( t) if L < Avo v( t) < L+ L i f L > Avo v( t) we fd the followg output signal condition: v out ( t ) d Avo v( t) Avo v( t) if < S. R. dt = d Avo v( t) ± ( SR..) t+ C if > SR.. dt

15 3/4/2011 Slew Rate lecture 4/7 For example For example, say we build a non-vertg amplifier with mid-band ga A vo = 2. This amplifier was constructed usg an op-amp with a slew rate equal to 4V/μsec. Q: If we put the followg signal v( t ), what will we see at the output of this amplifier? v ( ) t t (μsec) -2

16 3/4/2011 Slew Rate lecture 5/7 This is what it should look like A: Ideally, the output would look exactly like the put, only multiplied by A vo = 2: v ( t) = 2 v ( t) (ideal) v ( ) out t +4 out t (μsec) -4 Note that the time derivative of this output is zero at almost every time t : dv out dt ( t) = 0 for almost all time t

17 3/4/2011 Slew Rate lecture 6/7 Now you see the problem! The exceptions are at times t =4, t =8, and t =12 μsec, where we fd that the time derivative is fite! and dv out dt ( t) dv = at times t = 4 and t = 12 out dt ( t) = at time t = 8 This is a problem! v ( ) out t +4 dv out dt ( t) = > 4V/ μsec!!!! t (μsec) -4

18 3/4/2011 Slew Rate lecture 7/7 This is what it actually looks like! Thus, the output signal exceeds the slew rate of the op-amp or at least, it tries too! The reality is that sce the op-amp output cannot change at a rate greater than ± 4V/μsec, the output signal will be distorted! v ( ) o t +4 ideal slew-rate limited t (μsec) -4 Note the derivative of the actual output signal is limited to a maximum value ( 4V/μsec ± ) by the op-amp slew rate.

19 3/4/2011 Full Power Bandwidth lecture 1/7 Full-Power Bandwidth Consider now the case where the put to an op-amp circuit is susoidal, with frequency ω. The output will thus likewise be susoidal, e.g.: v ( t) = V sωt where V o is the magnitude of the output se wave. out o Q: Under what conditions is this output signal possible? In other words, might this output signal be distorted? A: First, the output will not be saturated if: Vo L+ V + and Vo L V.

20 3/4/2011 Full Power Bandwidth lecture 2/7 The time derivative Q: So, the output will not be distorted if the above statement is true? A: Be careful! It is true that the output will not saturate if magnitude of the sewave is smaller than the saturation limits. However, this is not the only way that the signal can be distorted! Q: I almost forgot! A signal can also be distorted by slew-rate limitg. Could this problem possibly affect a se wave output? A: Recall that the slew rate is a limit on the time derivative of the output signal. The time derivative of our se wave output is: dvout ( t) = ωvo cosωt dt

21 3/4/2011 Full Power Bandwidth lecture 3/7 The max and m Note that the time derivative is proportional to the signal frequency ω. Makes sense! As the output signal frequency creases, the output voltage changes more rapidly with time. Also note however, that this derivative is a likewise a function of time. The maximum value occurs when cosωt = 1, i.e,: dvout ( t ) dt max = ω V o while the mimum value occurs when cosωt = 1, i.e.,: dvout ( t ) dt m = ωv o Thus, we fd that the output signal will not be distorted if these values are with the slew rate limits of the op-amp.

22 3/4/2011 Full Power Bandwidth lecture 4/7 A simple way to determe you are slew rate limited In other words, to avoid distortion by slew rate limitg, we fd: and ω Vo S. R. ω V S. R. o Note that: 1) These two equations are equivalent! 2) The conditions that cause slew-rate distortion depend on both the magnitude V o and the frequency ω of the output signal!

23 3/4/2011 Full Power Bandwidth lecture 5/7 The frequency can only be so large Now, recall that there are limits on the magnitude alone, that is: V L V + o + to avoid saturation. Let s assume that the output se wave is as large as it can be without saturatg, i.e., V o = V + and thus: + vout ( t ) = V s ωt We then fd to avoid slew-rate limitg: ω V + < S. R. Rearrangg, a limit on the maximum frequency for this se wave output (one with maximum amplitude) is: SR.. ω < ω V + M

24 3/4/2011 Full Power Bandwidth lecture 6/7 The value: Full-Power bandwidth ωm = SR V + is called the full-power bandwidth of the op-amp (given a DC supply V + ). It eauals the largest frequency a full-power (i.e., V o = V + ) se wave can obta without beg distorted by slew rate limitg! Thus, if the put signal to ω V + < S. R. an op-amp circuit is a se wave, we might have to worry about slew rate limitg, if the signal frequency is greater than the full-power bandwidth (i.e., ω > ω ). M

25 3/4/2011 Full Power Bandwidth lecture 7/7 I ll fd out from the exam if you read this page Please note these important facts about full-power bandwidth: 1) The analysis above was performed for a se wave signal. It is explicitly accurate only for a se wave signal. For some other signal, you must determe the time derivate, and then determe its maximum (or mimum) value! 2) Full-power bandwidth is completely different than the closed-loop amplifier bandwidth. For example, a signal with a frequency greater than the closed-loop amplifier bandwidth will not result a distorted signal! 3) Distortion due to slew-rate limitg depends both on signal amplitude V + and signal frequency ω. Thus, as se wave whose frequency is much greater than the full-power bandwidth (i.e., ω ω ) may be undistorted if its amplitude V + is sufficiently small. M

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