Ch. 5: Analog Signal Processing Using Operational Amplifiers
What is a buffer/follower amp? Draw a schematic of one.
- an amp where V_out = V_in. - High input impedance causes the source to be isolated from the rest of the circuit. Connection: a transformer isolates circuit components Characteristics: - High input impedance - Low output impedance Essentially just a noninverting amp where R_F = 0 and R = ∞.
1) What is a differentiator op amp circuit? 2) Draw a schematic of one. 3) What is the output signal from the circuit?
1) an inverting amplifier where the input resistor is replaced by a capacitor. 2) See image. 3) Output = inverted, scaled derivative of the input signal
What are types of signal processing?
1. Amplification 2. Inversion 3. Differentiation 4. Integration 5. Addition 6. Subtraction 7. Comparison
What circuit components is the operational amplifier the building block for?
1. Amplifiers 2. Integrators 3. Summers 4. Differentiators 5. Comparators 6. A/D and D/A converters 7. Active filters 8. Sample and hold amplifiers In other words, to create any of the above elements, you start with an op amp and add to it. Connection: semiconductors are the building blocks for transistors
What are the key general relationship to note about gain, bandwidth, and GBP in a real op amp circuit?
1. As you increase the gain in the circuit, you decrease the bandwidth. 2. If your circuit only requires a small bandwidth and has low frequency input, you can use larger gains without worrying about the signal being attenuated or distorted.
What tools do you need to analyze a circuit that involves an op amp?
1. Ideal op amp equivalent circuit model 2. Kirchhoff's laws 3. Ohm's law
What are the 3 assumption that describe an ideal op amp? How to remember?
1. Infinite impedances at both inputs. - Thus, no current is drawn from the input circuits. 2. Infinite gain. - Difference between input voltages must be zero. (Represented by short between inverting and noninverting inputs) 3. Zero output impedance. - Output voltage does not vary with output current.
When designing or selecting an amplifier, what components are important to consider?
1. Size 2. Cost 3. Power consumption 4. Input impedance 5. Output impedance 6. Gain 7. Bandwidth
Explain why feedback happens when someone with a microphone stands too close to a loudspeaker.
A positive feedback loop is created that causes the loud squeal. The amplified sound from the loudspeaker goes back into the microphone and gets amplified again.
What is the ideal model of an op amp? What does it consist of? Notes? Draw and label the schematic for an ideal op amp.
An op amplifier that has: - A differential input, - A single output, and - Assumed to have infinite gain Consists Of: 1. Inverting input terminal (-) 2. Noninverting input terminal (+) 3. Output terminal (∞) Notes: 1) Voltages are all referenced to a common ground. 2) Active device (thus, requires connection to external power supply, not usually shown on schematic). 3) Since it is an active device, the output voltage and current can be larger than input.
Compare and contrast analog and digital signals.
Analog Signals: - Continuous - Infinite number of states or values - Signal produced by physical parameters Digital Signals: - Discrete - Finite number of states or values - Required for microcontrollers
5.10: Integrator
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5.11: Differentiator
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5.12: Sample and Hold Circuit
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5.13: Comparator
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5.14: The Real Op Amp
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5.1: Introduction
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5.2: Amplifiers
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5.3: Operational Amplifiers
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5.4: Ideal Model for the Operational Amplifier
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5.5: Inverting Amplifiers
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5.7: Summer
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5.8: Difference Amplifier
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How would you use an op amp to create a stable reference voltage? Why is the op amp needed in this circuit?
Components Needed: - Buffer/follower op amp - Supply voltage (> reference voltage) - Potentiometer You create a voltage divider where the second resistor is a potentiometer. This always you to change the resistance and have a wide range of reference voltages. Why the Buffer is Needed?: W/O: voltage output will vary based on the current flowing into the circuit W/: high impedance of buffer causes constant reference voltage output regardless of changes in the current flowing into the circuit.
Compare and contrast the difference amplifier and the instrumentation amplifier.
Difference Amplifier: - Only works for sources with low impedances - Input impedance is too low for large impedance sources - Cannot extract the difference signal btw input signals that are low level and include noise Instrumentation Amplifier: - Solves the problems associated with the difference amplifier - - Capable of amplifying low level signals in noisy environments
Compare and contrast a real op amp versus an ideal op amp.
Differences 1) Input impedance 2) Max output voltage 3) Response to step input 4) Frequency response Ideal: 1) Infinite input impedance 2) Maximum output voltage= max and min supply voltages (Ex. ±15V supplies = ±15 max, min output voltages) 3) Step input, step output 4) Infinite bandwidth Real: 1) Finite input impedance (large but no infinite) 2) Maximum output voltage: 1.4 volts less than max and min supply voltages (Ex. ±15V supplies = ±13.6 max, min output voltages) 3) Step input, output 4) Finite bandwidth: bandwidth is a function of the gain of the op amp
What effect does differentiation have on noise in the input signal? What effect does integration have on noise in the input signal?
Differentiation: - Amplifies/intensifies the fast-changing noise from the input into the output signal - Noise is problematic for differentiation circuits Integration: - Has a smoothing effect on the noise - Noise is not a concern when using an integrator
What is the input/output relationship for an inverting amplifier? What does this tell us?
Gain: (negative) 1) The voltage gain of the amplifier is determined exclusively by the values of the external resistors (R and R_F). 2) The voltage gain is ALWAYS negative.
What is the input/output relationship for a noninverting amplifier? What does this tell us?
Gain: ≥ 1 (positive) What It Tells Us: 1) Practical Use: Can isolate one portion of the circuit from another by transmitting a scaled voltage without pulling measurable current
What is the principal of superposition? Generally? What about in relation to analyzing amplifiers?
General: when there are multiple inputs applied to a linear system, the response to each individual input can be analyzed separately. The total result/response is then the sum of the individual results. Amplifiers: (Assuming ideal voltage and current sources) - To analyze the response from one source of multiple inputs, short all other ideal voltage sources and change all ideal current sources to open circuits.
5.6: Noninverting Amplifier
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5.9: Instrumentation Amplification
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In what type of application would a buffer/follower would be useful? Example? Why?
In a situation where you need to transfer a voltage signal without applying a load to the source providing that voltage. Example: voltage reference circuit
Discuss how amplitude linearity plays a role with amplifiers.
In most cases, you want to the gain to be constant across all frequency. This results in amplitude linearity. If an amplifier is designed to only amplifier certain frequencies, the result is a filtering effect. - The output voltage is then governed by the amplifier's bandwidth and cutoff frequencies.
What's the equation for the voltage output of a comparator op amp?
In other words, - A positive output saturation voltage means the input voltage is greater than the reference voltage - A negative output saturation voltage means the input is smaller than the reference voltage. Notes On Saturation Values: - Positive saturation values is slightly less than the positive supply voltage. - Negative saturation value is slightly larger than the negative supply voltage.
Ideally, what would happen to the output of a buffer amplifier if the input voltage was applied to the inverting input and feedback was from the output to the noninverting input?
Infinite gain and therefore an infinite output voltage.
Why is it called an inverting amplifier? Give an example.
It gets its name from the fact that the amplifier reverses the polarity of a signal. - For periodic waves, the result is a phase shift of 180
What is the output impedance of an amplifier? Equation? Analogy? What are typical values for the output impedance of an amplifier? Why?
It is a measure of how much the output voltage changes with a change in output current. - the ratio of the output voltage to the input current. Analogy: analogous to the output impedance of a voltage source Typically Output Impedance Values: Very small Why?: So output voltage will change very little as output current changes Connection: equation is same as Ohm's law
How does the improved integrator op amp circuit behave at different input frequencies?
Low Frequencies: behaves like an inverting amplifier Why?: Impedance of feedback loop is essential R_s since the impedance of C is very large at low frequencies High Frequencies: output is attenuated to zero. The capacitor acts like a short circuit. Why?: B/c the R_1C path in the circuit is effectively a low pass filter. Btw Low and High Frequencies: behaves as an integrator amp Why?:
With all IC's (integrated circuits), how are they labeled?
One end of the chip is marked with an indent or spot. With indent up and at the top of the IC and Starting at the pin to the left of the indent/spot with the number 1, the pins are numbered in a counterclockwise fashion.
What is a summer op amp? Draw a schematic of one.
Op amp used to add analog signals Gain: negative sum of the inputs (if all three resistor are equivalent)
What's the difference btw open-loop gain and closed-loop gain?
Open-loop gain: - Characteristic of an op amp W/O feedback Closed-loop gain: - Overall gain of an op amp W/ feedback - ALWAYS limited by the open-loop gain of op amp Example: In image, an op amp with a closed-loop gain of 100 would have a bandwidth of 0Hz-10,000Hz
How are op amps usually packaged? What is the typical manufacturer's designation of a general purpose op amp?
Packaged: 8-pin dual in-line package (DIP) integrated circuit (IC) Manufacturer's Designation: 741
A good example of positive feedback is when Jimi Hendrix used to move his guitar close to the front of his amplifier speaker. Explain what is happening here.
Playing a note on the strings causes the strings to vibrate, which is in-turn amplified by the speaker (amplifier). When the guitar is pointed towards the speaker, the sound from the amplifier causes the strings to vibrate more greatly (increases the V+ input) which gets fed back to the speaker and amplified again, even larger this time. It's effectively creating a positive feedback loop.
What's the difference between positive and negative feedback?
Positive: part of the output signal is added to the input signal. Feedback loop is from output to noninverting input (+). Negative: part of the output signal is subtracted from the input signal. Feedback loop is from output to inverting input(-).
What are common problems associated with signals produced by a transducer? Why do we have analog signal processing?
Problems (Signal not in desired form): 1. Signal is too small, (in millivolt range) 2. Signal is too noisy, (usually because of electromagnetic interference) 3. Contain incorrect info (due to poor design or install) 4. Contain a DC offset Analog signal processing: used to remedy the above problems.
What is a common mode rejection ratio (CMRR)? What is the CMRR in an ideal instrumentation amplifier? How to remember?
Ratio of amplification factors: ratio of the difference mode gain to the common mode gain. Ideally: common mode gain = 0, CMRR = ∞ How To Remember:
What is coupling in electronics? How to remember?
Simply the transfer of energy from one part of a circuit to another. It can be through direct wiring (DC case) or through non-contact (i.e. capacitor) Connection: sounds like "couple" - Couple holding hands (i.e. transferring energy, heat, via direct contact.) - Couple getting aroused (i.e. transfer of sexual energy, not necessary through contact)
How do you convert btw a triangular/sawtooth wave and a square wave?
Triangular to Square: differentiate the triangular wave Square to Triangular: integrate the square wave
What is an inverting amplifier? What does it do? What does it consist of? Schematic?
What It Does: - Inverts and amplifies the input voltage Consists Of: - Two external resistors connected to an op amp.
What is a noninverting amplifier? Schematic? How to remember?
What It Does: an amplifier that amplifies the input voltage without inverting the signal Consists Of: - Two external resistors connected to an op amp. (Exact same components as an inverting amp. The only difference is the two inputs are switched.) How to remember: (Where the voltage source V_in goes determines the type of amplifier: inverting versus noninverting) - The voltage source V_in always goes to the noninverting input of the op amp.
Why do most op amps contain a feedback loop? What's the difference between and op amp with a feedback loop versus one without?
Why: it provides stabilizes the amplifier and provides control of the gain Op Amp w/ a Feedback Loop: - Called a closed configuration - Stable amplifier - Linear behavior - Gain is controlled by loop - Common in most amplifiers Op Amp w/o a Feedback Loop: - Called an open configuration - Considerable instability in the amplifier - Nonlinear behavior - Very high gain - Rarely used
1) What is a sample and hold circuit? 2) Draw a schematic of one. 3) How does it work?
a circuit that stabilizes a signal while it is converted from an analog to a digital signal. Consists Of: - A voltage holding capacitor - A buffer/follower circuit - A switch How it Operates: - Switch Closed, Vout = Vin - Switch Open, capacitor holds the input voltage corresponding to the last sampled value. Used extensively in analog to digital (A/D) conversion.
What is an amplifier? How to remember?
a device that increases the amplitude of a signal without changing the phase relationships of the various components of the signal Connection: growth ray - Its essentially a growth ray that makes you bigger without say shifting your arm or leg "out of phase" or to a new location on you body.
What is relationship between open-loop gain and frequency? Draw a diagram showing the relationship.
a linear loglog relationship GBP is the sloped line
What is an operational amplifier (op amp)? What is the key to its utility? How did it get its name? What does it consist of? Imagery?
a low-cost and versatile integrated circuit (IC) "Workhouse of all analog electronics" - High gain - Feedback - Differential input Key to Utility: feedback Name: it got its name from its ability to perform so many different task. It is the building block for so many circuit elements. Connection: jack of all trades (mechie/EMT) of the amplifier world Consists of: many 1) internal transistors, 2) resistors, and 3) capacitors manufactured into a single chip of silicon. Imagery: an ideal op amp hugging an engineer and EMT
What type of capacitor should be chosen for the holding capacitor in a sample and hold amplifier?
a low-leakage capacitor. It's important that the voltage of the capacitor doesn't drop due to leakage during the hold period.
What is an analog signal?
a signal that is continuous and time varying
What is solid state technology? Examples? How to remember?
a technology where charge carriers (electrons) move through a solid semiconductor material Examples: - solid state transistors - solid state integrated circuits Connection: solid state = semiconductor
What is an instrumentation amplifier? Characteristics?
amp that solves the problems with the difference amp Characteristics: - Very high input impedance - Large CMRR - Capable of amplifying low level signals in noisy environments - Consistent bandwidth over a large range of gains
What is common mode gain? What is the common mode gain for an ideal difference amplifier? How to remember?
amplification factor for the average of the input signals - Want to minimize this value to suppress noise. - If common mode gain ≠ 0, output will be nonzero for two identical, nonzero inputs. Ideal Difference amplifier: common mode gain = 0 How to Remember: - common = average, gain = amplification factor
What is difference mode gain? How to remember?
amplification factor for the difference btw the input signals How To Remember: - difference = subtraction, gain = amplification factor
What is an improved integrator circuit? Draw a schematic of one.
an integrator circuit that contains a shunt resistor in parallel with the capacitor, and a pulldown resistor connected to the noninverting input.
1) What is a comparator circuit? 2) Draw a schematic of one.
an op amp circuit use to determine whether one signal is greater than the other. This op amp circuit does NOT contain a feedback loop and exhibits infinite gain (thus, the op amp saturates) Comparator op amps are designed to operate in saturation as comparators.
What are open-collector outputs in relation to op amps?
an op amp where the output is controlled by a transistor operating at saturation or cutoff.
What is the most basic model of an amplifier? Draw a diagram of a basic amplifier model.
as a 2-port device with: - Input voltage - Output voltage - Both are referenced to a ground
Draw the schematic for a comparator op amp with an open-collector output.
collector part of the transistor is not connected internally, and thus requires an external power connection. Transistor is on when V_in > V_ref Transistor is off when V_in < V_ref
What is a feedback loop? What is a closed loop configuration? Draw a schematic of an ideal op amp with a feedback loop.
feedback loop: a closed loop that goes from the output terminal of the op amp to the negative (inverting) input terminal - It always goes from output to negative input (this implies a negative feedback loop) closed loop configuration: simply an op amp that contains a feedback loop
What is the gain of an amplifier? Equation?
gain = the factor by which the voltage is changed A_v = voltage gain V_out = output voltage V_in = input voltage
1) What is an integrator circuit? 2) Draw a schematic of one. 3) What is the output of an integrator op amp circuit?
it is simply an inverting op amp circuit where the feedback resistor is replaced by a capacitor Output: Inverted, scaled integral of the input signal
What is the purpose of a shunt resistor in an improved integrator op amp circuit? Why is this important?
limit the low-frequency gain of the circuit. Why?: b/c even a small DC offset would be integrated over time which would eventually saturate the op amp.
What is the slew rate? How to remember?
maximum time rate of change possible for the output voltage. In other words, it's the slope of the output signal at the steps of a real op amp with a stepped input signal. How to Remember: "slew" also means skid - A real op amp "slews" a square wave input - Image: a square wave drive a car on snow covered roads and slewing/skidding/drifting around a corner
What is a difference amplifier? Schematic? How to remember?
op amp used to subtract analog signals. - Utilizes principle of superposition
What is gain bandwidth product (GBP)?
quantity used to quantify a real op amp's bandwidth's dependence on gain - A product of the open-loop gain and the bandwidth at that gain Characteristics: - Constant over wide range of frequencies. Image: the sloped line is the GBP Note: the gain decreases with increased input frequency
What are data sheets?
sheets that contain all of the information about an IC. They are provided by the manufacturer of the IC.
What is the rise time? How to remember?
the amount of time it takes for the output signal of a real op amp with an input stepped signal to go from 10% to 90% of its final value. - Value is specified by manufacturers How to Remember: - Time is always on the x-axis. Thus, its the x-component of the slew rate
What is the fall-off frequency?
the frequency where the open-loop gain curve first starts to limit the closed-loop gain. Imagery: an open loop op amp pushing a closed-loop op amp down a mountain when the closed-loop op amp climbs as high as the open-loop op amp - Elevation = gain
What is the input impedance of an amplifier? Equation? What are typical values for the input impedance of an amplifier? Why?
the ratio of the input voltage to the input current Analogy: analogous to the input impedance of a voltmeter Typically Input Impedance Values: - Very large so very little current is drawn from the input Connection: equation is same as Ohm's law
What is the simplest and most common form of signal processing? Define it.
Amplification: magnitude of the voltage signal is amplified
In relation to an op amp, what does saturation mean?
It means that the output remains in either its most positive or most negative output value.
