MULTIPLE CHOICE

- The current output (drain current, i
_{D}, from a field-effect transistor is controlled by two voltage differences: gate-source, V_{GS}, and drain-source, V_{DS}. Which of the following statements is**TRUE**?- The transconductance is the integral of i
_{D}over V_{DS}. - The transconductance is the partial derivative of i
_{D}with respect to V_{DS}(drain-source voltage). - The transconductance is the partial derivative of i
_{D}with respect to V_{GS}(gate-source voltage). - The transconductance is the partial derivative of i
_{D}with respect to the threshold voltage, V_{th}.

- The transconductance is the integral of i

- Operational amplifiers amplify the voltage difference between two input terminals (inverting, -, and non-inverting, +). Which of the following statements is
**NOT**an assumption about ideal behavior of op-amps?- The magnitude of the open-loop gain is infinitely large.
- The common mode rejection is zero, so there is no output voltage offset when the input terminals are at the same voltage.
- The bandwidth is from 0 Hz up to the corner frequency.
- The time lag in response to a step input voltage is infinitely small.

- Which of the following is
**FALSE**about an inverting amplifier, with no feedback, powered by a voltage between +8 and -8 V, with open-loop gain of 5000, and with a corner frequency of 10 kHz? Assume non-ideal (real-world) behavior and a grounded non-inverting terminal.- When the voltage input to the inverting (-) terminal is an alternating current with peak-to-peak amplitude of 4 mV and frequency of 1 Hz, the output voltage will be saturated.
- When the voltage input to the inverting (-) terminal is an alternating current with peak-to-peak amplitude of 1 mV and frequency of 1 Hz, the output voltage will 180 degrees phase-shifted from the input.
- When the voltage input to the inverting (-) terminal is an alternating current with peak-to-peak amplitude of 1 mV and frequency of 1 Hz, the output voltage peak-to-peak amplitude will be 5 V.
- When the voltage input to the inverting (-) terminal is an alternating current with peak-to-peak amplitude of 1 mV and frequency of 20 Hz, the output voltage will be saturated.

- What is the resolution of a 4-bit digital-to-analog converter with reference voltage of 5 V?
- 5/4 V
- 5/8 V
- 5/16 V
- 5/32 V

- In electrocardiography, two electrodes attached to the patient’s body detect small (millivolt) voltages caused by electrical conduction of the beating heart. The electrode leads insert into two voltage follower op-amps, which then connect to the inputs of a differential amplifier. Why are voltage followers placed between the electrodes and differential amplifier terminals?
- Voltage followers have a gain of 1, so they cancel out 60 Hz noise transmitted to the electrode leads by inductance.
- Voltage followers rectify the signal to be always positive.
- Voltage followers have a large input resistance, so they act as buffers tovariations in resistance at the electrodes that would otherwise “load” the differential amplifier.
- Voltage followers shift the phase of both inputs so there is always a voltage difference.

- What is the number 54 in base 2 (binary)?
- 111000
- 110110
- 101001
- 101011
- 101101

- How is a comparator used in an analog-to-digital converter?
- In a feedback loop, the comparator compares the analog signal, V
_{i}, to a reference voltage, V_{ref}, determining one bit value per loop by assigning a bit-value of 1if , V_{i}>V_{ref}, and a bit-value of 0 if V_{i}<V_{ref}. - In a feedback loop, the comparator amplifies the difference between V
_{i}and V_{ref}until saturation is reached. Digital logic is used to keep track of the number of loops performed, and each bit values is determined from the number of loops. - In a feedback loop, the comparater compares the analog signal, V
_{i}, to a reference voltage, V_{ref}, and feeds the information to a clock or “timer” circuit. The timer circuit converts the difference into a binary number. - In a feedback loop, the comparator compares the analog signal, V
_{i}, to a reference voltage, V_{ref}, determining one bit value per loop by changing V_{i}to match V_{ref}.

- In a feedback loop, the comparator compares the analog signal, V

- What is the impedance of a capacitor?
- 1/C
- 1/jC
- 1/jωC
- jωC

SHORT ANSWER

- (A) Draw the two Bode plots (amplitude, T(ω), and phase, φ(ω)) of the inverting amplifier of question 3. Assume that unity gain occurs at a frequency of 40 kHz. Include the corner frequency. T(ω) can be in decibels or unitless, and φ(ω) can be in radians or degrees. (B) on the amplitude Bode plot only, draw in the closed-loop gain frequency response of the op-amp when a feedback loop is added such that the maximum closed loop gain = 100? (C) What values of resistors would you use to create this closed loop gain of 100? You can call them R
_{F}and R_{i}, as in the class lectures.

- Draw the circuit diagrams for an inverting op-amp and a non-inverting op-amp. Label the terminals “-“ and “+”. Label the source voltage V
_{S}, the output voltage V_{O}, and the resistors R_{F}and R_{i}. Write the equations for the closed loop gain of each circuit, and draw a box around them. Then, write down values for V_{S}, R_{F}, and R_{i}. Solve for the closed loop gain and the output voltage, V Draw a box around your answers.

- A biosignal contains low-frequency drift (at 1-10 Hz, 100 mV amplitude), high frequency noise (at 60 Hz, 5 V amplitude), and the desired signal has an amplitude of 10 mV and a range from 15-50 Hz. Noise, drift, and signal all occur at the same time, and are all converted to electrical signals (voltages) by the sensor. How would you use circuits to filter out the noise and drift and amplify the desired signal? Please use both words and circuit diagrams.

LONG ANSWER

*DETECTING SEIZURES USING EEG*

- Electroencephalography (EEG) measures brain wave activity in a way similar to how an ECG measures cardiac activity. In one EEG setup, there are 18 electrodes attached to different spots on the surface of a patient’s head. The goal is to identify the type, duration, and magnitude of a seizure from the voltage recordings. An example of a seizure, recorded by EEG electrodes, is below. All 16 electrode channels change during the seizure, but the amplitude is different in each case.

- Describe how you would set up a signal processing circuit for each EEG channel. Include a voltage follower, an amplifier (choose between inverting, non-inverting, no feedback, or differential), a frequency filter (choose low-pass and/or high-pass), and an analog-to-digital converter. Draw a box diagram with arrows leading from the electrodes to the digital output that is sent to a computer, including each processing element along the way.
- How does skull thickness beneath the electrode change the voltage amplitude recorded by that electrode?
- You know the skull thickness underneath each electrode. What circuit will you use to scale the voltage from each lead so you can accurately compare signal amplitudes? Describe briefly.
- Say you want to count the number of times an EEG channel voltage is larger than some voltage threshold. What active circuit element would you use to perform this counting? Include a diagram of the output voltage versus the input (signal) voltage.

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**13.**

Write a circuit diagram for an inverting op-amp with feedback that contains resistors, and at least one capacitor, and one inductor. Solve for the frequency-dependence of the close-loop gain by replacing the resistance terms from the equation in class with the impedance of the equivalent circuit.