Questions and Answers
What is the main building block in all analog electronics?
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?
Gain bandwidth product (GBW)
An operational amplifier can have a ______ input or a ______ input.
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Match the following amplifiers with their characteristics:
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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?
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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?
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What is the effect of peaking in the frequency domain?
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What is the settling time?
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What is a generic 2-stage amplifier composed of?
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What is the characteristic of a first-order low-pass filter?
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What is the gain of a buffer?
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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?
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An opamp is a two-stage amplifier.
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What is the characteristic of a feedback system?
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What is the characteristic of a two-stage amplifier?
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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?
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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.
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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?
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What does GBW stand for?
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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.
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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?
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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 ________.
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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?
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How can the positive zero be eliminated?
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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.
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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'?
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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.
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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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Description
The operational amplifier (opamp) is a fundamental component in analog electronics. This quiz covers its implementation and application.