Slew Rate MCQ Quiz - Objective Question with Answer for Slew Rate - Download Free PDF

Explanation:

Slew Rate and its Significance:

The slew rate of an operational amplifier (op-amp) is defined as the maximum rate of change of output voltage per unit time. It is typically expressed in volts per microsecond (V/μs) or volts per millisecond (V/ms). The slew rate limits the ability of the op-amp to follow rapid changes in the input signal, causing distortion if the input signal frequency or amplitude exceeds certain limits.

In the given question, the op-amp has a slew rate of 62.8 V/ms and is connected in a voltage follower configuration. In this configuration, the output voltage ideally follows the input voltage exactly. However, when the input signal's rate of change exceeds the slew rate, the output cannot follow the input accurately, resulting in slew rate limited distortion.

Given Data:

• Slew rate of the op-amp (SR) = 62.8 V/ms
• Maximum amplitude of the sinusoidal input (V_m) = 10 V

Key Formula:

The maximum rate of change of a sinusoidal signal occurs at its peak (zero-crossing point), and it can be expressed as:

Rate of change of voltage = ω × V_m

where:

• ω = 2πf is the angular frequency of the signal
• f is the frequency of the sinusoidal signal
• V_m is the amplitude of the sinusoidal signal

The condition for avoiding slew rate limited distortion is:

ω × V_m ≤ SR

Substituting ω = 2πf, the condition becomes:

2πf × V_m ≤ SR

Rearranging for frequency (f):

f ≤ SR / (2π × V_m)

Solution:

Substitute the given values into the formula:

• SR = 62.8 V/ms = 62.8 × 10³ V/s (convert to V/s)
• V_m = 10 V
• 2π ≈ 6.28

Calculate the minimum frequency at which distortion sets in:

f = SR / (2π × V_m)

f = (62.8 × 10³) / (6.28 × 10)

f = 1 × 10³ Hz

f = 1 kHz

Therefore, the minimum frequency at which slew rate limited distortion sets in is 1 kHz. To convert this to MHz:

f = 1 kHz = 1 × 10⁻³ MHz = 1 MHz

Correct Answer: Option 1) 1 MHz

Important Information:

To further analyze the other options:

Option 2: 6.28 MHz

This option assumes a miscalculation in the formula. If the factor of 2π is misinterpreted, it might lead to this incorrect result. However, as shown in the detailed solution, the correct calculation yields 1 MHz, not 6.28 MHz.

Option 3: 10 MHz

This option is incorrect because it overestimates the frequency at which distortion sets in. The slew rate of the op-amp limits the maximum rate of change of the output voltage, and the correct calculation shows that distortion begins at 1 MHz, not 10 MHz.

Option 4: 62.8 MHz

This option is also incorrect and represents a significant overestimation. This value might come from a misunderstanding of the slew rate value itself or an error in applying the formula. The slew rate of 62.8 V/ms corresponds to a much lower frequency limit of 1 MHz for the given input amplitude of 10 V.

Conclusion:

The slew rate is a critical parameter in op-amp applications, especially in high-frequency or high-amplitude signal processing. For the given op-amp with a slew rate of 62.8 V/ms and an input amplitude of 10 V, the minimum frequency at which slew rate limited distortion sets in is 1 MHz. This frequency is calculated using the formula f = SR / (2π × V_m), ensuring accurate analysis of the op-amp's performance limits.

Slew Rate :

The maximum rate of change of output voltage .

Unit : volts per second

It decides maximum operable frequency of opamp.

let V_in = A sin 2πf_mt

V₀ = V_in = A sin 2πfmt

Slew Rate = \(\frac{dV_0}{dt}\) = A.2πf_m cos 2πfmt

\(\frac{dV_0}{dt}|_{max}\) = A.2πfm

Calculation :

10 V/µs  = A x 2 x π x 10⁶

10 V/10^-6  = A x 2 x π x 106

A = 5 / π 

Slew rate:

• The slew rate of an operational amplifier indicates how fast its output voltage can change.
• The output of an Op-Amp can only change by a certain amount in a given time. This limit is called the slew rate of the Op-Amp.
• Op-Amp slew rate can limit the performance of a circuit if the slew rate requirement is exceeded.
• This is best explained with the help of the given waveform:

Mathematical Analysis:

The maximum rate of change of the output voltage in response to a step input voltage is defined as the slew rate of the op-Amp.

Mathematically, the slew rate is defined as:

\(S.R = {\left( {\frac{{d{V_0}}}{{dt}}} \right)_{max}}\) V/µs

When the input is a sinusoid given as:

Vi (t) = Vm sin2πf t

The rate of change of input:

\(\frac{{d{V_i}}}{{dt}} = {{\rm{V}}_m}2{\rm{\pi }}{{\rm{f}}}{\rm{cos}}2{\rm{\pi }}{{\rm{f}}}{\rm{t}}\)

The maximum rate of change will be:

|Vm 2πf cos2πf t|max

\({\left. {\frac{{{d_{Vi}}}}{{dt}}} \right|_{max}} = {V_m}2\pi {f} =Slew~Rate\)

Key Points

•  The slew rate is defined as the maximum rate of output voltage change per unit of time. (Denoted by letter S)
• The slew rate helps us to identify the amplitude and maximum input frequency suitable to an operational amplifier such that the output is not significantly distorted.
• It should be as high as possible to ensure the maximum undistorted output voltage swing.
• Formula:

                                 \(S=\frac{\mathrm{d} V_{0}}{\mathrm{d} x}\bigg\rvert_{maximum} \, \, Volts/ \mu S\)

Concept:

When the input is a sinusoid given as:

Let, the gain of OPAMP is 'Av', the output is given as:

Vo(t) = Av Am sin(2πfmt)

The rate of change of output:

\(\frac{{d{V_o}}}{{dt}} = A_v A_m ~cos (2π f_m t)\)

The maximum rate of change = |Av A 2πfm cos(2πfmt)|max

\({\left. {\frac{{{d{V_o}}}}{{dt}}} \right|_{max}} = {A_v}A_m~2π {f_m} =Slew~Rate\)

Calculation:

Slew rate : 10 × 0.5 × 2π × 25 × 10³ = 785 × 10³ V/s 

= 0.785 V/μs

Concept:

Slew rate is the maximum rate of change of output voltage with respect to time.

Slew rate limits the maximum frequency of operation of op-amp

The slew rate is usually measured in volts per microsecond.

Mathematically,

Vin = Vm sin 2πfmt and

V0 = AVin

then, Slew rate = \({\left( {\frac{{d{V_0}}}{{dt}}} \right)_{max}} = 2{\rm{\pi }}{{\rm{f}}_{{\rm{max}}}}{{\rm{V}}_0}_{{\rm{max}}}{\rm{\;}}\)

∴ We can say that the signal bandwidth fm is limited by the Slew rate.

Calculation:

Slew rate \(= \frac{{{\rm{\Delta }}{V_0}}}{{{\rm{\Delta }}{V_i}}} × \frac{{{\rm{\Delta }}{V_i}}}{{{\rm{\Delta }}t}} = {A_{CL}}\left( {2\pi {f_m}{V_m}} \right)\)

Given that, slew rate = 62.8 V/μsec

62.8 × 10⁶ = 6.28 × 10 × f_m 

f_m = 1 MHz

Slew rate:

• The slew rate of an operational amplifier indicates how fast its output voltage can change.
• The output of an Op-Amp can only change by a certain amount in a given time. This limit is called the slew rate of the Op-Amp.
• Op-Amp slew rate can limit the performance of a circuit if the slew rate requirement is exceeded.
• This is best explained with the help of the given waveform:

Mathematical Analysis:

The maximum rate of change of the output voltage in response to a step input voltage is defined as the slew rate of the op-Amp.

Mathematically, the slew rate is defined as:

\(S.R = {\left( {\frac{{d{V_0}}}{{dt}}} \right)_{max}}\) V/µs

When the input is a sinusoid given as:

Vi (t) = Vm sin2πf t

The rate of change of input:

\(\frac{{d{V_i}}}{{dt}} = {{\rm{V}}_m}2{\rm{\pi }}{{\rm{f}}}{\rm{cos}}2{\rm{\pi }}{{\rm{f}}}{\rm{t}}\)

The maximum rate of change will be:

|Vm 2πf cos2πf t|max

\({\left. {\frac{{{d_{Vi}}}}{{dt}}} \right|_{max}} = {V_m}2\pi {f} =Slew~Rate\)

Concept:

Slew rate

It is the maximum rate of change of output voltage for all possible input signals.

It is defined as:

\(SR = {\left| {\frac{{d{V_0}}}{{dt}}} \right|_{max}}\frac{{volts}}{{\mu sec}}\) 

Calculation:

Given slew rate is 5 V/ms and the rate of change of the input signal is 0.2 V in 10 ms

\(\frac{{d{V_0}}}{{dt}} = \frac{{5V}}{{ms}}\) 

\(\frac{{d{V_{in}}}}{{dt}} = \frac{{0.2}}{{10\;ms}}\) 

Required voltage gain is

\(\frac{{{V_0}}}{{{V_{in}}}} = \frac{{\frac{{d{V_0}}}{{dt}}}}{{\frac{{d{V_{in}}}}{{dt}}}}\) 

\(\frac{{{V_0}}}{{{V_{in}}}} = \frac{{d{V_0}}}{{dt}} \times \frac{{dt}}{{d{V_{in}}}}\) 

\(\frac{{{V_o}}}{{{V_{in}}}} = \frac{5}{{1\;ms}} \times \frac{{10\;ms}}{{0.2}}\) 

\(\frac{{{V_0}}}{{{V_{in}}}} = \frac{{50}}{{0.2}}\) 

Slew Rate:

• Slew rate is the maximum rate of change of output voltage with respect to time.
• Slew rate limits the maximum frequency of operation of op-amp
• The slew rate is usually measured in volts per microsecond.

Mathematically:

Vin = Vm sin 2πfmt and

V0 = AVin

∴ The Slew rate will be:

\({\left( {\frac{{d{V_0}}}{{dt}}} \right)_{max}} = 2{\rm{\pi }}{{\rm{f}}_{{\rm{max}}}}{{\rm{V}}_0}_{{\rm{max}}}{\rm{\;}}\)

Since the slew rate is the ratio of voltage and time, they are expressed as V/sec.

Also, since the time period is usually very small (in μsec), the slew rate is commonly expressed as V/μsec.

Slew Rate :

The maximum rate of change of output voltage .

Unit : volts per second

It decides maximum operable frequency of opamp.

let V_in = A sin 2πf_mt

V₀ = V_in = A sin 2πfmt

Slew Rate = \(\frac{dV_0}{dt}\) = A.2πf_m cos 2πfmt

\(\frac{dV_0}{dt}|_{max}\) = A.2πfm

Calculation :

10 V/µs  = A x 2 x π x 10⁶

10 V/10^-6  = A x 2 x π x 106

A = 5 / π 

• The output of an Op-Amp can only change by a certain amount in a given time. This limit is called the slew rate of the Op-Amp.
• Op-Amp slew rate can limit the performance of a circuit if the slew rate requirement is exceeded.
• This usually happens at high frequencies, i.e. when the rate of change of signals is large.
• When the rate of change is large, it becomes difficult for the Op-Amp to track such fast variations.

This is best explained with the help of the given waveform:

The Slew-Rate of an Op-Amp for a give sinusoidal input is given by:

Slew Rate = 2π.f.V

Where,

f = The Highest signal frequency component (in Hz).

V = the maximum peak voltage of the signal.

Slew rate:

• The slew rate of an operational amplifier indicates how fast its output voltage can change.
• The output of an Op-Amp can only change by a certain amount in a given time. This limit is called the slew rate of the Op-Amp.
• Op-Amp slew rate can limit the performance of a circuit if the slew rate requirement is exceeded.
• This is best explained with the help of the given waveform:

Mathematical Analysis:

The maximum rate of change of the output voltage in response to a step input voltage is defined as the slew rate of the op-Amp.

Mathematically, the slew rate is defined as:

\(S.R = {\left( {\frac{{d{V_0}}}{{dt}}} \right)_{max}}\)

When the input is a sinusoid given as:

Vi (t) = Vm sin2πf t

The rate of change of input:

\(\frac{{d{V_i}}}{{dt}} = {{\rm{V}}_m}2{\rm{\pi }}{{\rm{f}}}{\rm{cos}}2{\rm{\pi }}{{\rm{f}}}{\rm{t}}\)

The maximum rate of change will be:

|Vm 2πf cos2πf t|max

\({\left. {\frac{{{d_{Vi}}}}{{dt}}} \right|_{max}} = {V_m}2\pi {f} =Slew~Rate\)

Slew rate is the maximum rate of change of output voltage with respect to time.

Slew rate limits the maximum frequency of operation of op-amp

The slew rate is usually measured in volts per microsecond.

Mathematically,

Vin = Vm sin 2πfmt and

V0 = AVin

then, Slew rate = \({\left( {\frac{{d{V_0}}}{{dt}}} \right)_{max}} = 2{\rm{\pi }}{{\rm{f}}_{{\rm{max}}}}{{\rm{V}}_0}_{{\rm{max}}}{\rm{\;}}\)

∴ We can say that, the signal bandwidth fm is limited by the Slew rate.

Concept:

Slew rate is defined as the maximum rate of change of output voltage per unit of time under large-signal conditions.

i.e. \(SR = {\left. {\frac{{d{V_o}}}{{dt}}} \right|_{max}}V/\mu s\) 

Calculation:

Given that, i_max = 150 μA

C = 100 pF

Considering a charging current of a capacitor i_max

\({i_{max}} = C\frac{{dV}}{{dt}}\) 

Hence, \(\frac{{dV}}{{dt}} = \frac{{{i_{max}}}}{C} = \frac{{150\mu }}{{100p}} = 1.5\;V/\mu s\)

Concept:

When the input is a sinusoid given as:

Let, the gain of OPAMP is 'Av', the output is given as:

Vo(t) = Av Am sin(2πfmt)

The rate of change of output:

\(\frac{{d{V_o}}}{{dt}} = A_v A_m ~cos (2π f_m t)\)

The maximum rate of change = |Av A 2πfm cos(2πfmt)|max

\({\left. {\frac{{{d{V_o}}}}{{dt}}} \right|_{max}} = {A_v}A_m~2π {f_m} =Slew~Rate\)

Calculation:

Slew rate : 10 × 0.5 × 2π × 25 × 10³ = 785 × 10³ V/s 

= 0.785 V/μs