LINEAR INTEGRATED CIRCUITS Unit3 Raghudathesh VTU

8/17/2019 LINEAR INTEGRATED CIRCUITS Unit3 Raghudathesh VTU

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AC Freq Response Raghudathesh G P Asst Professor

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LINEAR INTEGRATED CIRCUITS (VTU) - 10EC46

UNIT - 3

Op-Amps frequency response and compensation: Circuit stability, Frequency and phase

response, Frequency compensating methods, Bandwidth, Slew rate effects, Zin Mod

compensation, and circuit stability precautions.

6 Hours

TEXT BOOKS:

1. “Operational Amplifiers and Linear IC’s”, David A. Bell, 2nd

edition, PHI/Pearson, 2004.

2. “Linear Integrated Circuits”, D. Roy Choudhury and Shail B. Jain, 2nd

edition, Reprint 2006,

New Age International.

Special Thanks To:

Faculty:

BY:

RAGHUDATHESH G P

Asst Prof

ECE Dept, GMIT

Davangere 577004

Cell: +917411459249Mail: [email protected]

Website: raghudathesh.weebly.com

Quotes:

To lose patience is to lose the battle.

You just can´t beat the person who never gives up.

The pessimist sees difficulty in every opportunity. The optimist sees opportunity in every

difficulty. Do not settle for less than an extraordinary life.

I am a great believer in luck, and I find that the harder I work the more luck I have.

mailto:[email protected]








Introduction: Op-amp has an internal phase shifts from input to output.

Phase shifts are greatest at high frequencies and at some particular frequency the total

phase shift can add up to 360°. When this happens, the op-amp circuit is likely to become

unstable enough to break into oscillation. For oscillation to occur, the loop voltage gain (the product of the voltage gain ‘M’ and

the feedback factor ‘β’) must be equal to, or greater than, unity when the phase shift

approaches 360°.

To prevent instability, compensating capacitors and resistors are used either to reduce the

voltage gain or to minimize the phase shift.

The upper cutoff frequency of an operational amplifier circuit depends upon the

particular op-amp employed and upon the compensating components.

The frequency response is also limited by the op-amp slew rate. Some IC operational

amplifiers (notably the 741) have internal compensation which makes them very easy touse but limits the frequency response.

Op-Amp Circuit Stability: Consider an inverting amplifier circuit and waveforms shown in figure 3.1(a).

Figure 3.1(a): Inverting Amplifier

The input signal voltage Vs is amplified by a factor R 2/R 1 and phase shifted by an angle -

180°.





Consider the below circuit which is redrawn in figure 3.1(b)

Figure 3.1(b): Inverting Amplifier Oscillating

Above show that output voltage Vo is divided by the feedback network to produce

feedback voltage Vf .

Whether or not an input signal is present, any AC voltage at the op-amp inverting input

terminal is amplified by the open-loop gain M to produce an output voltage V o and then

divided to produce a feedback voltage Vf .

Suppose an AC voltage Vf occurs at the inverting input terminal. The amplified Vf is Vo

= MVf and the divided Vo is Vf = βVo. Neglecting signal source resistance R s,

If βVo is exactly equal to and in phase with the original V f , the circuit is supplying its

own AC input and a state of continuous oscillation exists.

The circuit in figure 3.1(a) can be redrawn with input voltage Vsis grounded and is shown

in figure 3.1(b).

Output voltage Vo is divided to produce a feedback voltage Vf which is applied to the

amplifier inverting input terminal.

Oscillation of the circuit is quite possible, because of the feedback network, virtually

every operational amplifier circuit act as a potential oscillator.

Frequency compensation are the measures which are taken to prevent oscillation.





Some operational amplifiers, such as the 741, are internally compensated. These

amplifiers have limited frequency response and are unsuitable for many applications.

When an uncompensated amplifier is employed, it is usually necessary to connect

external components to stablize the circuit.

Frequency and Phase Response:

Single stage Amplifier Response: The voltage gain of a single-stage transistor amplifier commences to fall off at some high

frequency. This may be due to the construction of the individual transistor or to stray

capacitance in the circuit.

Figure 3.2(a) shows a single-stage transistor amplifier circuit.

Figure 3.2(a): single-stage transistor amplifier

Figure 3.2(b) shows the high frequency ends of the gain/frequency and phase/frequency

responses of the circuit.





Figure 3.2(b): high frequency ends of the gain/frequency and phase/frequency responses

Note the frequency is plotted to a logarithmic base.

The voltage gain falls off at a rate of 6 dB for each doubling of frequency. This is also be

stated as a fall of 20 dB for each ten times increase in frequency. The pole frequency (fp)

is the frequency at which the gain is down by 3 dB from the mid-band gain. From the graph of phase-shift versus frequency [broken line in figure 3.2(b)], it is seen

that the phase lag increases from zero to -45° at the pole frequency. As the frequency

increases, the lag continues to increase to a maximum of - 90°.

Operational Amplifier Response: Operational amplifiers generally have a differential input stage, an intermediate

amplification stage, and a low impedance output stage as shown in figure 3.3(a) below.

Figure 3.3(a): An operational amplifier has three stages of amplification

Each of these three stages has its own gain/frequency and phase/frequency response.

The pole frequency (f p2) of Stage 2 is higher than the pole frequency (f pl) of Stage 1; and

the pole frequency (f p3) of Stage 3 is higher still.





A straight line approximation of the gain/frequency response graph for a typical

operational amplifier is shown in figure 3.3(b). This is known as a Bode plot.

Figure 3.3(b): Straight-line approximation of op-amp open-loop gain/frequency and phase/frequency responses

The overall voltage gain (M) initially falls off at 6 dB/octave (-20 dB/decade) from f p,

when only the gain of Stage 1 is decreasing. At f o, Stage 2 gain is decreasing at 6

dB/octave, so the total rate of de-cline is 12 dB/octave (-40 dB/decade). Finally, when the

frequency reaches fo, the gain of Stage 3 is decreasing at 6 db/octave and the overall rate

of decline of M is 18 dB/octave (-60 dB/decade).

The phase shifts of each stage also add together to give the total phase shift for the op-

amp.

A typical phase shift versus frequency (θ/f) response is shown as a broken line in figure

figure 3.3(b).

At fp1 the Stage 1 phase shift is -45° while the phase shift for each of the other two

stages is negligibly small, so the total phase shift is -45°.

At fp2 Stage 2 adds another -45°. But at this point the Stage 1 phase shift is at its

maximum of -90°. Consequently, the total phase shift at f p2 is

When the frequency is fp3, Stage 1 and Stage 2 are each contributing -90° of phase shiftand Stage 3 adds a further -45°. Thus, the total phase shift at fp3 is

This open-loop phase shift is additional to the -180° phase shift that normally occurs

from the op-amp inverting input terminal to the output.





Phase Margin: In an amplifier the difference between phase shift ϕ and 360

o at a frequency where M/Av

= 1 is called phase margin.

Oscillations occur in an op-amp circuit when the loop gain Mβ is equal to or greater than

1 and the loop phase shift is -360°. The phase shift does not have to be exactly -360° for oscillation to occur.

A loop phase shift of -330° at Mβ ≥ 1 makes the circuit unstable.

To avoid oscillations the total loop phase shift must not be greater than - 315° when Mβ =

1.

The difference between 360° and the actual phase shift at Mβ = 1 is referred to as the

phase margin. So for stability,

Consider phase shift ϕ = 200

o when M/Av = 1or Mβ = 0 dB then phase margin is

Larger the phase margin better is the amplifier stability.

For an amplifier, at Mβ = 1 or Av = M, phase delay will be close to 360 o; then the

amplifier may oscillate.

To avoid oscillation an external circuit is added to increase the phase delay ϕ beyond

360o at Av = M. this technique is known as frequency compensation.

Gain Margin: When the phase shift ϕ of Mβ = M/ Av is 180o or (360o) in an amplifier, the difference

between loop gain (Mβ) and unity is called gain margin.

High Gain Amplifier Stability: For an op-amp with the frequency response shown in figure 3.3(b), the maximum gain is

100 dβ which is equivalent to a voltage gain of 100000.

The overall voltage gain of an amplifier with negative feedback is

The loop gain is given as,





Thus,

Suppose an op-amp with a frequency response as in figure 3.3(b) is used with feedback to produce an amplifier with a closed loop gain of 70 dB. A horizontal line drawn on the

frequency response graph at Av = 70 dB intersects the open-loop gain/ frequency graph at

frequency f x.

At this point, Av = 70 dB and M = 70 dB. Consequently, the loop gain is

Thus, the frequency f x at which the closed-loop gain Av equals the open-loop gain M, is

the frequency at which the loop gain is Mβ = 1. This is one of the conditions required for

oscillation and which is the first condition of the circuit to become unstable.

Now the loop phase shift at frequency f x. From the intersection of the vertical line drawn

from f x and the θ/f graph, θ = - 120°. Because of the - 180° phase shift between the op-

amp inverting input terminal and the output, the total loop phase shift (ф) is

Phase margin is

For Av = 70 dB and Mβ = 1, the phase margin is 60°.

The minimum phase margin for stability is 45°, this particular circuit is likely to be stable

hence circuit will not oscillate.

At frequencies lower than f x, loop gain Mβ is greater than 1 but the open-loop phase shiftwill be smaller than - 120° then circuit will not break into oscillation.

For frequencies greater than f x, the loop gain Mβ < 1. Thus, the circuit will not break into

oscillation at higher frequencies.





Stability of Lower Gain Amplifiers:

Consider an amplifier with a voltage gain of 50 dB that uses an op-amp with the

frequency response in figure 3.4.

Figure 3.4: Straight-line approximation of op-amp open-loop gain/frequency and phase/frequency responses

A horizontal line drawn on the frequency response graph at Av = 50 dB intersects the

open-loop gain/frequency graph at frequency f Y where M = 50 dB, thus loop gain is given

as,

Hence at frequency f Y, one of the condition for the amplifier to become unstable is

satisfied.

Now let a vertical line at frequency f Y intersects the phase characteristics at point ‘P’. A

horizontal line drawn at ‘P’ corresponds to a phase shift (θ) of -165o. Also, the phase shift

introduced by the inverting amplifier is -180o. Hence total Phase shift (ф) is,

Hence, the phase margin is given as,





With AV = 50 dB at Mβ = 1, the phase margin is 15°. The phase margin is less than

minimum phase margin of 45° hence it is not adequate for stability, so the circuit is likely

to oscillate.

With AV = 70 dB, there is less feedback and the circuit is stable and amplifier with A V =

50 dB is unstable.

From above we see that amplifier with the higher close loop gain is stable and the one

with the lower closed-loop gain is unstable. This because for AV = 70 dB the feedback

network has an attenuation of β ≈ 70 dB while for AV = 50 dB the network attenuation is

β ≈ 50 dB.

The lower attenuation of the feedback network gives a greater amount of feedback and

thus makes oscillations more likely.

This discussion implies that an op-amp circuit with a low closed-loop gain is more

difficult to stabilize than one with a high closed-loop gain. The voltage follower, with a

gain of 1, is one of the most difficult circuits to stabilize.

Frequency Compensating Methods:

Introduction:

In order to prevent the unstable condition and to provide stability to op-amp, we mustensure:

1. The phase shift is less than 180o when loop gain (Mβ) = 1 or

2. The phase shift must be 180o when loop gain (Mβ) < 1.

Techniques which are employed to achieve the above is called as ‘frequency

compensation techniques, and op-amp is said to be frequency compensated.

Two methods which are employed to stabilize Op-amp circuits are:

1. Lag Compensation

2. Lead Compensation

For each method a resistance-capacitance network is connected into the circuit so that itis part of the loop. Usually, as recommended by the device manufacturer, the network is

connected to specified points within the op-amp.

For the above purpose, external terminals are provided for access to points within the IC.





Phase lag Compensation:

Figure 3.5 (a) below shows a phase lag compensation network.

Figure 3.5 (a): Lag Compensation Network

At lower frequencies, XC1 >> R 2 then voltage V2 lags V1. A phase lag of -90o might be

introduced.

At higher frequencies, XC1<< R 2 and the network becomes pure resistive network and no phase lag occurs. But at higher frequencies the phase lag network introduces some

attenuation and no phase lag is introduced as shown in figure 3.5 (b)

Figure 3.5 (b): Effect of lag compensation on gain/frequency response

The compensation of the phase lag network (R 1, R 2 and C1) are calculated to introduce

additional phase lag at lower frequencies. At higher frequencies there is only attenuation

without any additional phase lag.

The effect of the lag network attenuation is to move the frequency f x1 at which Mβ = 1

for a given closed-loop gain Av, to a lower frequency f x2.

As f x2 << f x1, the phase shift introduced by op-amp at f x2 will be less than at f x1. Due tothis, the phase margin increases and the circuit is unlikely to break into oscillations.

Despite its name, the lag network is not used to introduce a phase lag, (which would,

increase the total phase lag in the loop). Instead, it is employed to attenuate the loop gain,

so that Mβ = 1 occurs at a frequency at which the amplifier phase shift is too small to

cause oscillations.





Phase-Lead Compensation:

Figure 3.6 (a) below shows a phase lead compensation network.

Figure 3.6 (a): Lead Compensation Network

At lower frequencies, XC1 >> R 2 then voltage V2 leads V1.

Unlike the case of the lag network which is used only for attenuation, the phase lead

network is actually employed to introduce a phase lead.

The phase lead cancels some of the unwanted phase lag in the op-amp as shown in figure

3.6 (b) below

Figure 3.6 (b): Effect of lead compensation on gain/frequency response

This increases the phase margin at Mβ = 1, and improves the circuit stability.





Miller Effect Compensation:

Consider a common-emitter transistor amplifier stage with a capacitor connected between

its collector and base terminals as shown in figure 3.7 (a). Amplification and phase

inversion occurs. When Vi goes positive, Vo moves in a negative direction by an amount

AvVi.

------ (1)

Figure 3.7 (a): Single-stage transistor amplifier with capacitor between input and output

When the base voltage goes up by Vi and the collector voltage goes down by AvVi, the

voltage change across capacitor C1 is obtained by applying KVL from Vi, Vc and Vo

------ (2)

Put equation (1) in equation (2) we get,

The charge supplied to the capacitor is,

------ (3)





Thus, when the transistor base voltage changes by Vi, capacitor C1 is charged. The charge

is not Q = C1Vi, as might be expected, but Q = C1(1 + Av)Vi. Thus, the capacitance

appears to be amplified by a factor of (1 + Av). This is known as Miller effect.

The above reasoning can also be applied to the op-amp inverting amplifier circuit

illustrated in figure 3.7 (b) to show that C1 is amplified by a factor of (1 + Av). In thiscase, Av is the closed-loop gain of the amplifier.

Figure 3.7 (b): Op-amp inverting amplifier with capacitor between input and output

A capacitor and resistor connected in the same way as C1 and R 1 in figure 3.7 (a) are used

for frequency compensation inside the 741 op-amp. Figure 3.7 (c) shows that in this

situation the circuit behaves as a lag network. Compare this to figure 3.7 (a). The

advantage here is that the capacitance is amplified by the Miller effect, so a very small

value capacitor (30 pF for the 741) can be used.

Figure 3.7 (c): R1 and (1 + Av)C1 in (a) above constitutes a lag network for signal voltages





In the case of the externally connected Miller-effect capacitor in figure 3.7 (b), the

combination of C1 and R 1 behaves as a phase lead network within the feedback loop. This

is illustrated in figure 3.7 (d).

Figure 3.7 (d): R1 and C1 in (b) above constitutes a lead network for feedback voltages

The capacitance amplification is not a factor here because the direction of feedback is

from the output to the input and there is no capacitance amplification in that direction.

Thus, C1 and R 1 in figure 3.7 (d) introduce a phase lead to cancel some of the phase lag in

the loop.

Feed forward Compensation:

In feed forward compensation a capacitor is connected between the input and output

terminals of the high-gain stage of the op-amp. At high frequencies the high gain op-amp stage introduces large amount of phase shift to

the input signal.

The capacitor connected across op-amp compensates this phase to some extent thereby

reducing the large phase shift.

Op-Amp Circuit Bandwidth:

Cutoff Frequencies Introduction:

Operational amplifiers are directly coupled internally. When the signal and load are alsodirect-coupled, the circuit lower cutoff frequency is zero.

In capacitor-coupled circuits, the lower cutoff frequency is determined by the selection of

capacitors.

The circuit upper cutoff frequency is dependent upon the frequency response of the op-

amp, the compensating components, and the circuit voltage gain.





Upper Cutoff Frequency Determination:

For any operational amplifier circuit, the frequency at which the open-loop gain is equal

to the closed-loop gain upper cut-off frequency.

The upper cutoff frequency (f 2) is the frequency at which the closed-loop voltage gain

falls to 3 dB below the normal mid-frequency gain. The voltage gain of an amplifier with

negative feedback is

------ (1)

The open-loop phase shift of the op-amp progressively increases with increase in signal

frequency. Thus, equation (1) is written as

------ (2)

Looking at the open-loop phase/frequency and gain/frequency responses for the 741 op-

amp in figure 3.8 below. It is seen that because of the internal compensation, the phase

shift for the 741 remains at -90° for much of the frequency range during which the gain is

falling by 20 dB per decade.

Figure 3.8: Open-loop gain/frequency and phase/frequency responses for a 741 operational amplifier.

Substituting -90° for θ in the equation (2) for closed-loop gain gives





Now when M = Av = 1/β, then closed loop gain is

Thus, the upper cut-off frequency f 2 occurs at M = Av.

Gain-Bandwidth Product (GBP):

The gain-bandwidth product of an op-amp is the closed-loop gain Av, multiplied by the

cutoff frequency for that gain.

Unity gain Frequency (f u):

The frequency at which Av = 1 is called as Unity gain Frequency and denoted as f u.

Unity Gain Bandwidth (UGB) Product:

The gain bandwidth corresponds to f u is referred as Unity gain Bandwidth and is given as

Slew Rate Effects:

Definition: The slew rate (S) of an operational amplifier is the maximum rate at which theoutput voltage can change.





When large output voltages are involved, the circuit upper cutoff frequency is likely to be

substantially lower than for small signal circuits. This is due to the op-amp slew rate.

Figure 5-14(a) shows a sinusoidal output voltage waveform from an op-amp and

illustrates the fact that the fastest rate of change of the waveform occurs as the voltage

crosses zero.

Figure 3.9 (a): Sine wave maximum rate of change

At this point, maximum rate of change,

Here,

f = frequency

V p = peak amplitude

The kind of waveform distortion that occurs when the slew rate is too slow for the output

amplitude and frequency is illustrated for sine wave in figure 3.9 (b) below

Figure 3.9 (b): Slew Rate limited Sine Wave





For a distortion-free output, the op-amp slew rate (S) must be equal to, or greater than,

the maximum rate of change of the waveform. Thus, it is given as

Slew rate-limited frequency for a given output amplitude is given as

For a given cutoff frequency (f 2), slew rate-limited distortion free output amplitude is

given as,

Slew Rate Effect on Output Pulse Rise Time and Amplitude: When a pulse-type signal is to be amplified, the output rise time is related to the circuit

cutoff frequency. The equation for cutoff frequency limited rise time is

A pulse waveform can also be distorted by the op-amp slew rate as shown in figure 3.10

below

Figure 3.10: Slew Rate limited Pulse Output





The output rise time and amplitude are directly related to the slew rate. The equation for

slew rate limited rise time is

The slew rate can be said to limit the minimum output rise time for a given output

amplitude. Alternatively, it can be stated that the slew rate limits the output amplitude for

a given rise time.

Problems:

1. Calculate

a. The slew-rate limited cutoff frequency for a voltage follower circuit using a 741 Op-amp,

if the peak sinusoidal output is to be 5 V.

b. The maximum peak value of the sinusoidal output voltage that will allow the 741 voltage

follower circuit to operate at 800 kHz unity-gain cutoff frequency. Given S = 0.5 V/µs.

c. The maximum peak value of sine wave output voltage that can be produced by the

amplifier if the upper cut-off frequency is 8 kHz. June 2011 (5 M), June 2014 (6 M)

Solution:

Given: S = 0.5 V/µs, V p = 5 V, f 2 = 800 kHz

a. Slew rate-limited frequency for a given output amplitude is given as

b. For a given cutoff frequency (f 2), slew rate-limited output amplitude is given as,





c. For a given cutoff frequency (f 2 = 8 kHz), slew rate-limited maximum output amplitude is

given as,

2. Calculatea. The cutoff frequency limited rise-time for a voltage follower circuit using a 741 Op-amp.

b. Also determine the slew-rate limited rise time if the output amplitude us to be 5 V.

Given: S = 0.5 V/µs, f 2 = 800 kHz.

c. Calculate the minimum output rise time and the maximum pulse amplitude at that rise

time for a 741 amplifier with an upper cutoff frequency of 100 kHz. June 2011 (3 M), June

2012 (4 M)

Solution:

(a) Equation for cutoff frequency limited rise time is,

(b) The equation for slew rate limited rise time is





(c) Equation for minimum output rise time is,

Equation for maximum pulse amplitude at that rise time is,

3. Determine the upper cutoff frequency for a (i) voltage follower, (ii) unit gain inverting

amplifier using a 741 Op-amp. Given that Unity Gain Bandwidth (UGB) of 741 is 800 kHz.

December 2012 (4 M)

Solution:

(i) Expression for upper cutoff frequency for Unity gain Bandwidth is,

------- (1)

(i) Voltage gain of voltage follower is unity hence,

(ii) Expression for voltage gain of inverting amplifier is,





For unit gain inverting amplifier R 2 = R 1 thus,

Substituting Av in equation (2) we get,

4. Determine the upper cut-off frequency and maximum distortion free output amplitude

of a voltage follower when a 741 op-amp is used. December 2013 (4 M)

Solution:Given Av = 1, f u = 800 kHz, S = 0.5 V/µs

Expression for upper cutoff frequency is given as,

Expression for maximum distortion free output amplitude of a voltage follower is,

Stray Capacitance Effects

Circuit Instability Due to Stray Capacitance:

Stray capacitance can occur anywhere in a circuit. However, the worst place for stray

capacitance in an op-amp circuit is at the inverting input terminal. An inverting amplifier with stray capacitance Cs between the inverting and non-inverting

input terminals is shown in figure 3.11(a) below





Figure 3.11 (a): Stray capacitance at the op-amp input terminals can cause circuit instability

Figure 3.11(b) shows that the resistance seen when looking back from the capacitance

into the resistor network

Figure 3.11 (b): The stray capacitance Cs combines with the network resistance R to constitute a lag network

Resistance seen when looking back from the capacitance into the resistor network is

given as,

When R 3 is not present and R 5 is very much smaller than R 1,

The stray capacitance CS and the network resistance R constitute a phase lag net-work.

This introduces additional phase lag in the feedback loop which might cause circuit

oscillations.





The circuit starts oscillating if an phase lag introduces by the stray capacitance as small

as 6o in addition to the 30

o phase margin used by the circuit manufacturer with the

recommended compensating components.

Figure 3.12: A phase lag network introduces a lag of 45° when Xc = R and a lag of approximately 6° when Xc = 10 R

Analysis of a CR-phase shift network in figure 3.12 (a) shows that when XC = R, the

voltage across C lags the applied voltage by 45° as shown in figure 3.12 (b).

When XC = 10 R, the phase lag is approximately 6° as shown in figure 3.12 (c).

Thus, in the case of stray capacitance at the op-amp input, the circuit might become

unstable when

----- (1)

Here,

f = frequency at which Mβ = 1, the frequency at which the circuit is likely

to oscillate

In the above equation we see that

When very large value resistors are used in the op-amp circuit. Consequently, the

calculated value of CS is quite small.

When small value resistors are used, CS comes out as a larger value capacitance.

This means where the largest possible resistor values are used with an op-amp circuit, a

very small quantity of input stray capacitance might make the circuit oscillate. When

small resistor values are employed, relatively large amounts of stray capacitance must

occur before the circuit becomes unstable.





Therefore, for greatest circuit stability the smallest possible resistor values should be

selected.

Circuit stability can be further improved if resistor R 3 in figure 3.11 (a) is eliminated to

reduce the total calculated value of R. Where this is not possible, R 3 might be bypassed

with a capacitor which has an impedance much smaller than R 3 at the frequency at whichMβ = 1.

Compensating for Stray Capacitance:

Stray capacitance effects can be minimized by using the lowest possible resistor values.

The stray capacitance can also be kept low by keeping connecting leads short at the op-

amp input terminals. The bodies of resistors connected to these terminals should be

positioned close to the terminals so that the connecting leads can be kept as short as

possible.

Compensation for stray capacitance at an op-amp input can be provided by means of a

capacitor connected (C2) across the feedback resistor as shown in figure 3.13 below.

Figure 3.13: A feedback capacitor (C2) employed to compensate for the effects of stray capacitance

To eliminate the phase shift introduced by stray capacitance CS, the division of the output

voltage produced by Cs and C2 in series must be equal to that caused by resistors R 1 and

R 2. Thus,





----- (1)

Above equation does not allow for resistor R 3 and signal source resistance R s. If R 3 must

be in a circuit that requires this type of compensation, it should be by-passed. Where R s is

not much smaller than R 1, it should be added to R 1 in equation (1). Another way of

writing equation (1) is

This can be stated as: The time constant C2R 2 should be equal to, or greater than, the time

constant CSR 1.

Zin Mod Compensation:

The input impedance modification (Zin Mod) technique of frequency compensation is

normally used only as a method of increasing the bandwidth of an op-amp circuit.

This method is illustrated in figure 3.14 (a) below, involves the connection of a resistor

(R 4) and capacitor (C4) across the op-amp input terminals.

Figure 3.14 (a): Zin mod technique of frequency Compensation Technique

The capacitor serves only to AC couple R 4 into the circuit. So, C4 is selected to have an

impedance much smaller than the resistance of R 4 at the frequency at which Mβ = 1.





Thus, at the possible oscillation frequency of the circuit (and higher), R 4 appears in

parallel with R 1 to give the feedback network illustrated in figure 3.14 (b)

Figure 3.14 (b): Neglecting R s and R 3, the feedback network is changed by Zin Mod as shown

For simplicity, R 3 is assumed to be a short-circuit and Rs is taken to be much smaller than

R 1. Without R 4 and C4 in the circuit, the feedback factor is

With R 4 in the circuit, the feedback factor becomes

For circuit stability, the op-amp gain is now

The voltage gain of inverting amplifier remains





Without the use of R 4 and C4, the gain of the amplifier will be Av = 1/β. With the use of

R 4 and C4, β’ > β hence 1/β’ is more.

The compensating components are actually selected according to higher gain which

increases the bandwidth.

Due to presence of R 4 and C4 input impedance of op-amp is modified hence the method iscalled Zin Mod Compensation.

The input impedance is very high and is given as,

Circuit Stability Precautions:

Feedback along supply lines is another source of o p-amp circuit instability. This is

minimized by connecting 0.01 µF high frequency supply-decoupling capacitors from

each supply terminal to ground, as shown in figure 3.15 below.

Figure 3.15: Operational Amplifier Circuit Stability




Asst Professor raghudathesh weebly com Page | 30

These must be connected right at the IC terminals. Sometimes one pair of decoupling

capacitors can be used with several op-amps which use the same supply lines and which

are located close together. In some cases, 0.1 µF capacitors might be necessary.

The following list of precautions should be observed for op-amp circuit stability:

1.

Where only low frequency circuit performance is required, use an internallycompensated operational amplifier like the 741.

2. Keep all component leads as short as possible and take care with component

placement. Resistors connected to When using an op-amp that must be

compensated, use the manufacturer's recommended methods and components.

Where possible use over-compensation.

3. the op-amp input terminals should have the body of the resistor placed close to the

input terminal.

4. Use 0.01 µF high frequency capacitors to bypass the supply terminals of op-amp

(or groups of op-amp) to ground. Connect these capacitors close to the ICterminals.

5. Always have the signal source connected to a circuit to be tested. Alternatively,

ground the circuit input.

6. Do not connect oscilloscopes or other instrument at the op-amp (inverting or non-

inverting) input terminals.

7. If a circuit is unstable after all of the above precautions have been observed,

reduce the value of all circuit resistors (except compensating resistors). Also,

reduce the signal source resistance if possible. Then, if necessary, try

compensating for stray capacitance or load capacitance, as appropriate.

8. If the circuit bandwidth is not large enough with the recommended compensating

components, try Zin Mod.

Read Yourself Instability due to Output Capacitance

LINEAR INTEGRATED CIRCUITS Unit3 Raghudathesh VTU

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