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Definitions & Key Concepts
Learn essential terms and foundational ideas that form the basis of the topic.
Key Concepts
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Resistor Emulation: Replacing a physical resistor with a switched capacitor and clock.
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Discrete-Time Operation: Integration occurs in steps, not continuously.
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Advantages in ICs: Area saving, precise ratio matching, programmability (via $f\_{CLK}$), CMOS compatibility.
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Critical Components: Op-Amp, $C\_S$, $C\_F$, Analog Switches, Two-Phase Clock.
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Non-overlapping Clock: Essential to prevent short circuits.
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Examples
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SC Filter: Beyond integrators, switched capacitor techniques are widely used to build highly accurate filters (low-pass, high-pass, band-pass) in ICs. Their cutoff frequencies can be tuned by changing the clock.
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Charge Pump: Another common SC circuit used to generate higher or lower DC voltages from a supply, particularly for flash memory or gate drivers.
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Sample-and-Hold Circuit: SC techniques are fundamental to the design of sample-and-hold circuits found at the input of many ADCs.
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Building Your Own Clock: You could use a 555 timer to generate a square wave, and then use a D-flip-flop and some gates to create two non-overlapping phases ($\phi\_1$ and $\phi\_2$) for the CD4066 switches.
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Flashcards
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Term: Switched Capacitor
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Definition: A circuit technique using capacitors and switches driven by a clock to emulate resistors and other analog components.
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Term: $R\_{eq}$ (Equivalent Resistance)
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Definition: The resistance mimicked by a switched capacitor, given by $1/(f\_{CLK} \times C\_S)$.
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Term: Non-Overlapping Clock
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Definition: A pair of clock phases ($\phi\_1, \phi\_2$) used in SC circuits where both are never high simultaneously, preventing shorts.
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Term: IC Area Saving (SC)
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Definition: An advantage of SC circuits where they use smaller capacitors to replace large resistors, reducing the physical size of ICs.
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Term: Programmability (SC)
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Definition: The ability to control circuit parameters (like cutoff frequency or integration rate) by digitally changing the clock frequency.
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Memory Aids
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"Capacitor is a Clock-Controlled Resistor": The core idea: a capacitor (C) acts like a resistor (R) when rapidly switched by a clock.
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"SC = Silicon Chip Saver": Switched Capacitors are great for Silicon Chips because they Save area and improve Control.
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"No Overlap, No Oops\!": The clock phases must be non-overlapping to prevent accidental short circuits ("oops\!").
Examples & Real-Life Applications
See how the concepts apply in real-world scenarios to understand their practical implications.
Examples
-
SC Filter: Beyond integrators, switched capacitor techniques are widely used to build highly accurate filters (low-pass, high-pass, band-pass) in ICs. Their cutoff frequencies can be tuned by changing the clock.
-
Charge Pump: Another common SC circuit used to generate higher or lower DC voltages from a supply, particularly for flash memory or gate drivers.
-
Sample-and-Hold Circuit: SC techniques are fundamental to the design of sample-and-hold circuits found at the input of many ADCs.
-
Building Your Own Clock: You could use a 555 timer to generate a square wave, and then use a D-flip-flop and some gates to create two non-overlapping phases ($\phi\_1$ and $\phi\_2$) for the CD4066 switches.
-
-
Flashcards
-
Term: Switched Capacitor
-
Definition: A circuit technique using capacitors and switches driven by a clock to emulate resistors and other analog components.
-
Term: $R\_{eq}$ (Equivalent Resistance)
-
Definition: The resistance mimicked by a switched capacitor, given by $1/(f\_{CLK} \times C\_S)$.
-
Term: Non-Overlapping Clock
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Definition: A pair of clock phases ($\phi\_1, \phi\_2$) used in SC circuits where both are never high simultaneously, preventing shorts.
-
Term: IC Area Saving (SC)
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Definition: An advantage of SC circuits where they use smaller capacitors to replace large resistors, reducing the physical size of ICs.
-
Term: Programmability (SC)
-
Definition: The ability to control circuit parameters (like cutoff frequency or integration rate) by digitally changing the clock frequency.
-
-
Memory Aids
-
"Capacitor is a Clock-Controlled Resistor": The core idea: a capacitor (C) acts like a resistor (R) when rapidly switched by a clock.
-
"SC = Silicon Chip Saver": Switched Capacitors are great for Silicon Chips because they Save area and improve Control.
-
"No Overlap, No Oops\!": The clock phases must be non-overlapping to prevent accidental short circuits ("oops\!").
Memory Aids
Use mnemonics, acronyms, or visual cues to help remember key information more easily.
🧠 Other Memory Gems
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The core idea: a capacitor (C) acts like a resistor (R) when rapidly switched by a clock.
* "SC = Silicon Chip Saver"
🧠 Other Memory Gems
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The clock phases must be non-overlapping to prevent accidental short circuits ("oops\!").
Flash Cards
Review key concepts with flashcards.
Glossary of Terms
Review the Definitions for terms.
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Term: CMOS (Complementary MetalOxideSemiconductor)
Definition:
A dominant technology for fabricating integrated circuits, known for low power consumption.
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Term: Nonoverlapping Clock
Definition:
Essential to prevent short circuits.
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Term: Building Your Own Clock
Definition:
You could use a 555 timer to generate a square wave, and then use a D-flip-flop and some gates to create two non-overlapping phases ($\phi\_1$ and $\phi\_2$) for the CD4066 switches.
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Term: Definition
Definition:
The ability to control circuit parameters (like cutoff frequency or integration rate) by digitally changing the clock frequency.
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Term: "No Overlap, No Oops\!"
Definition:
The clock phases must be non-overlapping to prevent accidental short circuits ("oops\!").
Detailed Explanation
The Switched Capacitor (SC) Integrator represents an advanced topic in analog circuit design, particularly relevant for understanding how analog functions are implemented efficiently and accurately within integrated circuits (ICs). Traditional Op-Amp integrators use a resistor at the input, but large, precise resistors are problematic to fabricate on silicon. Switched Capacitor circuits ingeniously overcome this.
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Understand the Principle (Review Section 4.2.4):
- Before construction, it's crucial to have a firm grasp of the theoretical foundation.
- Resistor Emulation: The core idea is that a small capacitor ($C\S$) rapidly switched between two points can mimic the behavior of a much larger resistor. When connected to an input voltage, it charges. When connected to a summing junction (like the inverting input of an Op-Amp integrator), it discharges, transferring a discrete "packet" of charge. The average current transferred over time is proportional to the input voltage and the switching frequency ($f\{CLK}$), effectively creating an equivalent resistance $R\{eq} = 1/(f\{CLK} \times C\_S)$.
- Integrator Application: By replacing the fixed input resistor of a continuous-time Op-Amp integrator with this switched capacitor "resistor," you create a discrete-time integrator. This means the integration happens in steps, synchronized with the clock, rather than smoothly over time.
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Basic SC Integrator Construction (If components available):
- Components Required:
- Operational Amplifier (Op-Amp): A general-purpose Op-Amp (e.g., LM741, TL082) configured as an integrator. Power it with a dual supply (e.g., +/-12V or +/-15V).
- Capacitors: You'll need at least two capacitors:
- Sampling Capacitor ($C\_S$): A small capacitor (e.g., 1 nF to 10 nF, ceramic for non-polarity) that will be switched.
- Feedback Capacitor ($C\_F$): The capacitor in the Op-Amp's feedback loop (e.g., 10 nF to 100 nF, ceramic). The ratio $C\_S/C\_F$ determines the gain of the integrator per clock cycle.
- Analog Switches: At least two analog switches are needed to control the charging and discharging of $C\_S$. A common choice is a CMOS analog switch IC like the CD4066 (Quad Bilateral Switch) or similar. These ICs contain multiple switches that can be opened or closed by a digital control voltage.
- Two-Phase Non-Overlapping Clock Generator: This is critical. The switches need to be controlled by two clock phases ($\phi\_1$ and $\phi\_2$) that are non-overlapping. This means when $\phi\_1$ is high, $\phi\_2$ is low, and vice-versa, with a small "dead time" where both are low. This prevents short-circuiting input and output. You can create this using:
- 555 Timers: Two 555 timers configured as astable multivibrators or one 555 timer and some logic gates to generate the two phases.
- Logic Gates: Combinations of NOT, AND, OR gates, or a simple flip-flop could be used if you have a base clock source.
- Function Generator: Some function generators might have dual-phase outputs or you could use two separate generators and manually set their phase, though precise non-overlap is hard to achieve manually.
- Circuit Assembly:
- Build the Op-Amp integrator core: Inverting input connected to ground via R (optional for DC bias stability, or directly to ground if SC circuit handles bias). Feedback capacitor ($C\_F$) connected between output and inverting input.
- Integrate the SC resistor: Connect $C\_S$ and the analog switches to mimic the input resistor. A common configuration involves switching $C\_S$ between the input voltage and the Op-Amp's inverting input (summing junction) with the two clock phases.
- Connect the clock generator outputs to the control pins of the analog switches.
- Connect the input DC voltage to the SC input.
- Ensure all ICs (Op-Amp, analog switches, clock logic) are correctly powered (+/-Vcc for Op-Amp, +Vcc/GND for digital ICs) with proper decoupling capacitors.
- Components Required:
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Observation on the Oscilloscope:
- Apply power to the circuit.
- Apply a constant DC input voltage to the SC integrator.
- Observe the output of the Op-Amp on the oscilloscope.
- Expected Behavior: Instead of a smooth, continuous ramp (like a traditional RC integrator), you should observe a staircase-like output. Each "step" in the staircase corresponds to one clock cycle (or pair of phases) where a charge packet is transferred, causing a discrete change in the output voltage. The overall trend should still be a linear ramp, but it will be made of distinct steps.
- Varying Parameters:
- Clock Frequency ($f\_{CLK}$): Vary the clock frequency and observe its effect on the integration rate. Increasing $f\{CLK}$ should make the integration faster (steeper steps, or more steps per second if viewing a long-term ramp), because $R\{eq}$ becomes smaller ($R\{eq} = 1/(f\{CLK} \times C\_S)$).
- Input Voltage ($V\_{in}$): Change the DC input voltage. A higher input voltage should result in a faster integration rate (larger steps or steeper slope).
- Capacitor Values ($C\_S, C\_F$): If possible, try different ratios of $C\_S/C\_F$. The integration constant depends on this ratio.
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Discussion and Analysis (Section 11.E):
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Comparison to Continuous-Time Integrator:
- Similarities: Both types of integrators produce an output that is proportional to the time integral of the input signal, resulting in a ramp for a constant DC input.
- Differences:
- Continuous vs. Discrete: Continuous-time integrators produce a smooth, continuous output ramp. SC integrators produce a staircase-like output, integrating in discrete steps synchronized with the clock.
- Component Implementation: Continuous-time integrators use a physical resistor. SC integrators use a switched capacitor network to emulate a resistor.
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Primary Advantages of Switched Capacitor Circuits in IC Design:
- Area Saving: In ICs, large, precise resistors (especially high-value ones) consume significant silicon chip area. Capacitors, even when scaled down, are much more area-efficient for achieving equivalent resistance values. This reduces chip size and cost.
- Accuracy and Matching: While absolute capacitor values might vary slightly due to manufacturing, the ratio of two capacitors on the same IC can be controlled with extremely high precision (e.g., better than 0.1%). This is superior to achieving precise resistor ratios over a wide range. The performance of SC circuits depends primarily on precise capacitor ratios ($C\_S/C\_F$), leading to highly accurate filter characteristics, gains, or integration constants.
- Programmability: The equivalent resistance of a switched capacitor is inversely proportional to the clock frequency ($R\{eq}=1/(f\{CLK} \times C\_S)$). This means that the characteristics of the SC circuit (e.g., the cutoff frequency of a filter, or the integration rate of an integrator) can be easily programmed and controlled digitally simply by changing the clock frequency. This is a powerful feature not easily achieved with fixed-resistor circuits.
- Process Compatibility: Switched capacitor circuits are highly compatible with standard CMOS (Complementary Metal-Oxide-Semiconductor) manufacturing processes, which are dominant for digital ICs. This allows for easy integration of analog functions alongside digital logic on the same chip.
- Lower Power Consumption (in some cases): Since large resistors are avoided, power dissipation can be reduced in certain SC circuit designs.
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Comparison to Continuous-Time Integrator:
Quiz Questions
Choose the best answer for each multiple-choice question or indicate True/False. For fill-in-the-blank questions, provide the correct term.
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In integrated circuits, what is a primary benefit of using switched capacitor circuits instead of large, precise resistors?
a) Increased power consumption
b) Significant area saving
c) Reduced clock frequency requirements
d) Higher noise generation -
The equivalent resistance of a switched capacitor circuit is given by the formula $R_{eq} = 1 / (f_{CLK} \times C_S)$. Based on this, if the clock frequency ($f_{CLK}$) is doubled, the equivalent resistance will:
a) Double
b) Halve
c) Remain the same
d) Quadruple - True or False: Switched capacitor circuits allow for easy programmability of filter characteristics or gain values by simply changing the clock frequency.
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What type of electronic component typically acts as the "switch" in a switched capacitor circuit within an integrated circuit?
a) BJT
b) Diode
c) MOSFET
d) Resistor - A Switched Capacitor Integrator forms a \\\\\\\\\\\\\\\\ integrator, as opposed to the continuous-time behavior of a traditional Op-Amp integrator.
Solutions (Do not look until you've completed the practice questions!)
Exercise Solutions
Easy:
- The primary purpose of switched capacitor circuits in integrated circuits is to overcome the difficulty of fabricating large and precise resistors and capacitors. They achieve this by emulating these components using smaller capacitors, Op-Amps, and analog switches.
- Switched capacitor arrangements are primarily designed to mimic or replace resistors and, in the case of an integrator, effectively form a discrete-time integrator (which includes the function of a resistor at its input).
Medium:
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Principle of Mimicking a Resistor: A switched capacitor circuit mimics a resistor by rapidly switching a small capacitor ($C_S$) between an input voltage node and another node (e.g., a summing junction). When connected to the input, $C_S$ charges to the input voltage. When switched to the other node, it discharges, transferring a discrete packet of charge. By rapidly and repeatedly transferring these charge packets, an average current flows, which is proportional to the input voltage and the switching frequency. This average current flow effectively emulates the behavior of a resistor.
The formula for the equivalent resistance is:
$R_{eq} = \frac{1}{f_{CLK} \times C_S}$ Impact of Clock Frequency: If the clock frequency ($f_{CLK}$) is changed:
* If $f_{CLK}$ is increased, the capacitor is switched more rapidly, transferring charge packets more frequently. This leads to a decrease in the equivalent resistance ($R_{eq}$).
* If $f_{CLK}$ is decreased, the capacitor is switched less frequently, leading to an increase in the equivalent resistance ($R_{eq}$). -
The key components required for a basic Switched Capacitor Integrator are:
- Op-Amp: Functions as the core amplifier and current-to-voltage converter.
- Sampling Capacitor ($C_S$): The small capacitor that is switched to emulate a resistor.
- Feedback Capacitor ($C_F$): The capacitor that is charged by the transferred charge packets, performing the integration.
- Analog Switches: (e.g., MOSFETs in ICs, or ICs like CD4066) to rapidly connect/disconnect the sampling capacitor.
- Two-phase Non-overlapping Clock Generator: This generates the precise timing signals to control the opening and closing of the analog switches in a specific sequence, ensuring that charge transfer occurs correctly without short circuits.
Hard:
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Comparison of Output Behavior:
- Continuous-Time Op-Amp Integrator: Produces a continuous, smooth analog output voltage that changes over time based on the integral of the input voltage. The output voltage changes continuously with the input signal.
- Switched Capacitor Integrator: Produces a discrete-time (or sampled-data) output voltage. The output changes in distinct voltage steps, corresponding to each clock cycle or charge transfer event. While it still integrates the input, the output is not perfectly smooth but rather a staircase-like approximation that approaches the continuous integral at high clock frequencies.
1. Area Saving: Large resistors and capacitors are difficult and take up significant silicon area in integrated circuits. Switched capacitor circuits can emulate high resistance values using much smaller capacitors and switches, leading to more compact and cost-effective chip designs.
2. Accuracy and Matching: While absolute capacitor values might vary slightly during manufacturing, the ratios of capacitors can be precisely controlled and matched on an IC. Switched capacitor circuits' performance (e.g., gain, filter cutoff frequency) often depends on capacitor ratios rather than absolute values, leading to higher accuracy and better matching performance compared to resistor-based designs, especially for high-resolution applications.
3. Programmability: The effective "resistance" or integration rate of a switched capacitor circuit is directly controlled by the clock frequency ($R_{eq} = 1 / (f_{CLK} \times C_S)$). This allows for easy and precise programmability of filter characteristics, gain values, or ADC conversion rates simply by changing an external or internal clock signal, without needing to change physical components.
4. Process Compatibility: Switched capacitor circuits are highly compatible with standard CMOS fabrication processes, which are dominant in digital IC manufacturing. This allows for the integration of high-performance analog functions alongside digital logic on the same chip.
Quiz Answers
- b) Significant area saving
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b) Halve
- Since $R_{eq}$ is inversely proportional to $f_{CLK}$, doubling $f_{CLK}$ will halve $R_{eq}$.
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True.
- This is a key advantage, especially useful in programmable filters and gain stages.
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c) MOSFET
- MOSFETs (Metal-Oxide-Semiconductor Field-Effect Transistors) are commonly used as analog switches in integrated circuits due to their small size and easy integration.
- A Switched Capacitor Integrator forms a discrete-time integrator, as opposed to the continuous-time behavior of a traditional Op-Amp integrator.