GATE Biomedical Engineering Analog and Digital Electronics Syllabus

What is an instrumentation amplifier and why is it preferred for biomedical signals?

It is a precision difference amplifier (typically three op-amps) with very high input impedance, high CMRR, low noise, and an adjustable gain set by one resistor. These traits make it ideal for amplifying small differential bio-signals (ECG, EEG) in noisy environments.

Give the gain equation for the classic three-op-amp instrumentation amplifier.

$$\frac{V_{out}}{V_{2}-V_{1}} = \left(1+\frac{2R}{R_{gain}}\right)\frac{R_{3}}{R_{2}}$$ where $R_{gain}$ is the single external gain-setting resistor.

What is a voltage buffer (voltage follower) and what is its gain?

A buffer is a unity-gain amplifier ($V_{out}=V_{in}$, gain $=1$) with very high input impedance and very low output impedance. It isolates stages and prevents loading.

Why is impedance matching important and how does a buffer help?

A buffer's high input impedance draws negligible current from the source, and its low output impedance can drive a load without signal drop. This prevents the load from affecting the previous stage (loading effect).

Classify filters by the band of frequencies they pass.

Low-pass (passes below cutoff), High-pass (passes above cutoff), Band-pass (passes a band between two cutoffs), and Band-stop/Notch (rejects a band).

What is the difference between an active and a passive filter?

A passive filter uses only R, L, C with no gain (gain $\leq 1$). An active filter uses op-amps with R and C, can provide gain, avoids bulky inductors, and offers better isolation and tunability.

Give the cutoff frequency formula for a first-order RC filter.

$$f_{c} = \frac{1}{2\pi RC}$$ At this frequency the output is $-3\ \text{dB}$ ($\frac{1}{\sqrt{2}}$) of the passband value.

What is the quality factor Q of a band-pass filter?

$$Q = \frac{f_{0}}{BW} = \frac{f_{0}}{f_{H}-f_{L}}$$ where $f_{0}$ is the center frequency and $BW$ is the bandwidth. Higher Q means a narrower, more selective passband.

What is the Barkhausen criterion for sinusoidal oscillation in a waveform generator?

For sustained oscillation the loop gain magnitude must equal one and the total phase shift around the loop must be $0$ or $360^{\circ}$: $$|A\beta| = 1, \qquad \angle A\beta = 0^{\circ}$$

Give the frequency of oscillation of a Wien-bridge oscillator with equal R and C.

$$f = \frac{1}{2\pi RC}$$ The non-inverting amplifier requires a gain of at least 3 to sustain oscillation.

How does an astable multivibrator differ from a monostable and a bistable?

Astable: no stable state, free-running oscillator (generates square waves). Monostable: one stable state, produces a single pulse when triggered (one-shot). Bistable: two stable states, changes state only on triggering (flip-flop).

Convert the binary number $1011_{2}$ to decimal.

$$1011_{2} = 1\cdot2^{3}+0\cdot2^{2}+1\cdot2^{1}+1\cdot2^{0} = 8+0+2+1 = 11_{10}$$

How do you find the 2's complement of a binary number, and why is it used?

Invert all bits (1's complement) and add 1. It is used to represent signed numbers and to perform subtraction using addition in digital systems.

What are the radixes of binary, octal, decimal, and hexadecimal number systems?

Binary: base 2; Octal: base 8; Decimal: base 10; Hexadecimal: base 16. Each hex digit equals 4 binary bits; each octal digit equals 3 binary bits.

State De Morgan's two theorems in Boolean algebra.

$$\overline{A+B} = \bar{A}\cdot\bar{B}, \qquad \overline{A\cdot B} = \bar{A}+\bar{B}$$ The complement of a sum is the product of complements, and vice versa.

What are the Boolean identities for OR and AND with 0 and 1?

$$A+0=A,\quad A+1=1,\quad A\cdot0=0,\quad A\cdot1=A,$$ $$A+\bar{A}=1,\quad A\cdot\bar{A}=0,\quad A+A=A,\quad A\cdot A=A$$

Why are NAND and NOR called universal gates?

Any Boolean function (and all other gates AND, OR, NOT) can be implemented using only NAND gates or only NOR gates, so each alone is functionally complete.

Give the truth-table outputs (sum and carry) of a half adder.

$$\text{Sum} = A \oplus B, \qquad \text{Carry} = A\cdot B$$ It adds two single bits but cannot accept a carry-in.

What distinguishes a full adder from a half adder, and give its equations.

A full adder adds three bits (A, B, and carry-in $C_{in}$): $$\text{Sum} = A\oplus B\oplus C_{in}, \qquad C_{out} = AB + C_{in}(A\oplus B)$$

How is a half subtractor's difference and borrow expressed in Boolean form?

$$\text{Difference} = A\oplus B, \qquad \text{Borrow} = \bar{A}\cdot B$$

What is the function of a comparator (op-amp based)?

A comparator compares two voltages and outputs a logic high or low depending on which is larger. The op-amp runs open-loop, so a small input difference drives the output to saturation (+$V_{sat}$ or $-V_{sat}$).

What problem does a Schmitt trigger solve and how?

It eliminates noise-induced false switching near the threshold by adding hysteresis: it uses positive feedback to set two different threshold voltages (upper and lower trip points), so the output switches cleanly and is immune to small noise.

Define hysteresis (width of the dead band) for a Schmitt trigger.

$$V_{H} = V_{UT} - V_{LT}$$ the difference between the upper trip point and lower trip point voltages. Input must cross these distinct levels to change the output state.

What is a digital encoder?

An encoder is a combinational circuit that converts $2^{n}$ (or fewer) active input lines into an $n$-bit binary code. For example, an 8-to-3 encoder produces a 3-bit output for one of 8 active inputs.

What is a decoder, and how many outputs does an n-to-2^n decoder have?

A decoder converts an $n$-bit binary input into one of $2^{n}$ unique output lines (only one active at a time). An $n$-to-$2^{n}$ decoder has $2^{n}$ outputs; e.g., a 3-to-8 decoder has 8 outputs.

What is a priority encoder and why is it needed?

A priority encoder resolves the ambiguity when multiple inputs are active simultaneously by encoding only the highest-priority (highest-order) active input, unlike a simple encoder which gives invalid output for multiple active inputs.

What is the difference between a combinational and a sequential digital circuit?

A combinational circuit's output depends only on present inputs (no memory), e.g., adders, decoders. A sequential circuit's output depends on present inputs and past state (has memory), e.g., flip-flops, counters.

What is the slew rate of an op-amp and why does it matter?

Slew rate is the maximum rate of change of the output voltage: $$SR = \left.\frac{dV_{out}}{dt}\right|_{max}\ \left(\text{V}/\mu\text{s}\right)$$ It limits the maximum frequency/amplitude an op-amp can output without distortion.

What are the ideal op-amp assumptions used in circuit analysis?

Infinite open-loop gain, infinite input impedance (no input current), zero output impedance, infinite bandwidth, and zero offset. With negative feedback this gives the virtual short: $V_{+} = V_{-}$.

What is the gain-bandwidth product (GBW) of an op-amp?

$$\text{GBW} = A_{v} \times f = \text{constant}$$ For an op-amp the product of closed-loop gain and bandwidth is constant, so increasing gain reduces usable bandwidth.

Compare the input impedance and switching control of MOSFET vs BJT for biomedical/low-power use.

MOSFET has extremely high input impedance (gate draws ~no DC current) and is voltage-controlled, giving very low static power and easy integration. BJT is current-controlled with lower input impedance but higher transconductance for a given current, useful in precision analog stages.