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What is the main building block in all analog electronics?
What is the main building block in all analog electronics?
Operational amplifiers are required to be stable and provide a well-behaved response.
Operational amplifiers are required to be stable and provide a well-behaved response.
True
What is the key specification of an opamp that determines its performance?
What is the key specification of an opamp that determines its performance?
Gain bandwidth product (GBW)
An operational amplifier can have a ______ input or a ______ input.
An operational amplifier can have a ______ input or a ______ input.
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Match the following amplifiers with their characteristics:
Match the following amplifiers with their characteristics:
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What is the goal of designing an operational amplifier?
What is the goal of designing an operational amplifier?
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What is the factor that determines how high the peaking is in the frequency domain?
What is the factor that determines how high the peaking is in the frequency domain?
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What is the relation between the parameter Q and damping factor f?
What is the relation between the parameter Q and damping factor f?
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What is the consequence of having zero damping factor f?
What is the consequence of having zero damping factor f?
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What is the effect of peaking in the frequency domain?
What is the effect of peaking in the frequency domain?
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What is the settling time?
What is the settling time?
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What is a generic 2-stage amplifier composed of?
What is a generic 2-stage amplifier composed of?
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What is the characteristic of a first-order low-pass filter?
What is the characteristic of a first-order low-pass filter?
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What is the gain of a buffer?
What is the gain of a buffer?
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What is the characteristic of a high-pass filter?
What is the characteristic of a high-pass filter?
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What is the product of the open-loop gain A and the pole frequency f?
What is the product of the open-loop gain A and the pole frequency f?
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An opamp is a two-stage amplifier.
An opamp is a two-stage amplifier.
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What is the characteristic of a feedback system?
What is the characteristic of a feedback system?
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What is the characteristic of a two-stage amplifier?
What is the characteristic of a two-stage amplifier?
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What is the characteristic of a wideband amplifier?
What is the characteristic of a wideband amplifier?
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What is the term used to describe the distance of the phase characteristic from the critical -180° where oscillation can occur?
What is the term used to describe the distance of the phase characteristic from the critical -180° where oscillation can occur?
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What is the consequence of negative feedback converting into positive feedback at high frequencies in an opamp with two poles?
What is the consequence of negative feedback converting into positive feedback at high frequencies in an opamp with two poles?
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An amplifier with a phase margin of 90° is likely to exhibit peaking or oscillation.
An amplifier with a phase margin of 90° is likely to exhibit peaking or oscillation.
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Peaking or onset of oscillation is possible if the phase characteristic approaches the __________ line.
Peaking or onset of oscillation is possible if the phase characteristic approaches the __________ line.
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What is the purpose of the compensation capacitance in a two-stage opamp?
What is the purpose of the compensation capacitance in a two-stage opamp?
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What does GBW stand for?
What does GBW stand for?
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What determines the non-dominant pole's position for stability in operational amplifiers?
What determines the non-dominant pole's position for stability in operational amplifiers?
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The gain of the second stage in a two-stage opamp decreases with frequency.
The gain of the second stage in a two-stage opamp decreases with frequency.
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The non-dominant pole is mainly determined by the time constant C / _.
The non-dominant pole is mainly determined by the time constant C / _.
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What is the advantage of positioning the resistor R between 400 V and 1 kV on a logarithmic scale?
What is the advantage of positioning the resistor R between 400 V and 1 kV on a logarithmic scale?
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What is used to determine the Gain Bandwidth Product (GBW) in a two-stage amplifier?
What is used to determine the Gain Bandwidth Product (GBW) in a two-stage amplifier?
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In a single-stage amplifier, the load capacitance C determines the ________.
In a single-stage amplifier, the load capacitance C determines the ________.
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In a two-stage amplifier, there are two high-impedance points connected by a capacitance for polesplitting.
In a two-stage amplifier, there are two high-impedance points connected by a capacitance for polesplitting.
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What is the result of the feedforward through the compensation capacitance?
What is the result of the feedforward through the compensation capacitance?
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How can the positive zero be eliminated?
How can the positive zero be eliminated?
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Which technique does not require any biasing current to abolish the positive zero?
Which technique does not require any biasing current to abolish the positive zero?
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A large resistor in series with the compensation capacitance results in a negative zero.
A large resistor in series with the compensation capacitance results in a negative zero.
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How can we shift the non-dominant pole out to higher frequencies?
How can we shift the non-dominant pole out to higher frequencies?
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What is the main advantage of compensating an opamp with 'g' as opposed to 'C'?
What is the main advantage of compensating an opamp with 'g' as opposed to 'C'?
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Increasing the load capacitance will always require an increase in the compensation capacitance 'C'.
Increasing the load capacitance will always require an increase in the compensation capacitance 'C'.
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The phase for a second pole for a positive zero goes to ___ degrees.
The phase for a second pole for a positive zero goes to ___ degrees.
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What is one way to deal with the positive zero in opamp compensation?
What is one way to deal with the positive zero in opamp compensation?
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Study Notes
Operational Amplifiers
- An operational amplifier (opamp) is a main building block in analog electronics, usually implemented in a feedback loop to provide stable and predictable gain and low noise.
- An opamp is required to be stable and provide a well-behaved response, avoiding peaking in the frequency domain and ringing when a square waveform is applied.
Terminology and Basics
- Open-loop gain: the gain of the opamp without feedback.
- Closed-loop gain: the gain of the opamp with feedback.
- Two-stage amplifiers: a type of opamp with two stages, which can be affected by a positive zero.
- Single-transistor stages: a type of amplifier stage, already discussed in Chapter 2.
Operational Amplifiers and Analog Signals
- Opamps can perform operations on analog signals with great precision, such as addition, subtraction, and multiplication.
- The output voltage of an opamp is a precise sum of the input voltages, scaled by the corresponding resistors.
- High gain and low noise are essential specifications of an opamp.
Types of Operational Amplifiers
- Voltage opamp: has a differential voltage amplifier as an input and senses an input voltage.
- Current opamp: has a current input and is a current-current amplifier.
- Operational Transconductance Amplifier (OTA): a type of opamp that senses an input voltage and has a current output.
- Fully-differential amplifiers: used in mixed-signal environments to reject common-mode noise.
Stability of Operational Amplifiers
- Stability of an opamp is crucial, and its gain and bandwidth product (GBW) must be optimized for a certain capacitive load, towards minimum power consumption.
- GBW: the product of the open-loop gain and the bandwidth of an opamp.
Applications of Operational Amplifiers
- Opamps can be used to make various filters, such as integrators, low-pass filters, and high-pass filters.
- Inductors can be used to create high-pass filters.
- Opamps can be used to create various amplifier configurations, such as inverting amplifiers, non-inverting amplifiers, and buffers.
Internal Poles and Zeros of Operational Amplifiers
- An opamp always has one internal dominant pole, which occurs at a frequency f.
- The product of the open-loop gain A and the pole frequency f is the GBW.
- The GBW is the product of the gain and the bandwidth, for each setting of the gain.
- An opamp allows an exchange of gain for bandwidth, with the product being the GBW.### Feedback Systems and Operational Amplifiers
- A feedback system's properties are determined by the gain, which is the quantity that indicates how the input and output impedances change.
- An operational amplifier (opamp) is a single-pole system, allowing for exchange of gain with bandwidth within a specific GBW (Gain-Bandwidth Product).
- In a single-pole system, there is only one internal node at high impedance, and if there are more nodes at high impedance, there are more poles, making it a multi-pole system.
- Two-stage amplifiers have two high-impedance nodes and are therefore two-pole systems, requiring compensation to shift the non-dominant pole to higher frequencies.
Stability of Operational Amplifiers
- A truly single-pole amplifier can never show peaking or instability, maintaining a slope of -20 dB/decade and a phase of -90° for all frequencies beyond the bandwidth.
- The application of unity-gain feedback results in an amplifier with a bandwidth coinciding with the GBW, with no peaking or oscillation.
- The phase margin is the distance from the -180° line, and a phase margin of 90° is large enough to avoid peaking or oscillation.
Multi-Pole Systems and Peaking
- In a two-pole system, each pole causes a phase shift of -90°, resulting in a phase shift at high frequencies, and the signal is inverted.
- The phase margin decreases as the closed-loop gain decreases, and peaking occurs at high frequencies.
- The worst peaking occurs at the largest loop gain, i.e., for unity gain.
Compensating a Two-Pole Amplifier
- The objective is to shift the non-dominant pole to higher frequencies, eliminating the extra -90° phase shift and increasing the phase margin.
- Shifting the non-dominant pole to higher frequencies decreases peaking, and a phase margin of around 70° is desired to avoid peaking altogether.
Phase Margin and Peaking Calculations
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The phase margin and peaking calculations involve plugging the amplifier expression into the feedback expression for unity gain, and rewriting the coefficients in terms of resonant frequency and damping.
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The factor of three, which is the desired ratio of the non-dominant pole to the GBW, is a result of these calculations.
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The parameter Q is often used instead of damping, and values of damping between 0.5 and 1 are needed to avoid peaking.### Peaking and Stability in Operational Amplifiers
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Peaking in the frequency domain is related to ringing in the time domain.
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The amount of peaking in the frequency domain (P_f) and the amount of peaking in the time domain (P_t) are given.
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For a ratio of three between the non-dominant pole and the Gain-Bandwidth Product (GBW), the phase margin is 72°, corresponding to f = 0.87 (or Q = 0.57), with no peaking in the Bode diagram.
Phase Margin and Damping
- A damping factor f of 0.7 provides a maximally-flat response, while larger values reduce bandwidth and smaller values cause peaking.
- A value of three between the non-dominant pole and the GBW is a good safety position to start with.
- A damping factor f of 0.87 would not give any overshoot at all.
Ringing and Settling Time
- Ringing in the time domain corresponds to peaking in the frequency domain.
- The settling time is the time required to obtain the final value with a certain error.
- For a square waveform applied to a first-order system, the settling time is approximately 6.9 time constants.
- A damping factor f between 0.7 and 0.8 gives the best compromise between rise time and settling time.
Two-Stage Operational Amplifier
- A generic two-stage amplifier consists of a differential input stage and a second stage with a feedback capacitor (C_c).
- The gain (A) is the product of the input transconductance (g_m1) and the impedance of C_c.
- The gain decreases with frequency and crosses the unity-gain line at the GBW.
- The GBW is given by the frequency where the voltage gain is unity.
Stability and Non-Dominant Pole
- For stability, the position of the non-dominant pole is determined by the load capacitance (C_L) and the resistance seen by it.
- The non-dominant pole is mainly determined by the time constant C_L / g_m2.
- The correction factor C_c / C_L is typically taken to be 0.3.
- The f / GBW ratio must be about three for stability.
Design Techniques
- There are two possible design plans to shift the non-dominant pole, both with advantages and disadvantages.
- Both plans lead to pole splitting, which allows the non-dominant pole to be moved to even higher values.
- The stability requirement forces the positioning of the non-dominant pole at sufficiently high frequencies (around 3 GBW).
Small-Signal Equivalent Circuit
- The small-signal equivalent circuit is obtained by substituting the g-blocks with voltage-controlled current sources and adding node resistances.
- The low-frequency gains A_v1 and A_v2 are easily derived as products of g's and output resistances.
- The total gain A is the product of A_v1 and A_v2.
- The gain expression is of second order, despite the presence of three capacitances, due to the capacitive loop.
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The operational amplifier (opamp) is a fundamental component in analog electronics. This quiz covers its implementation and application.
