TS PGECET 2023 Biomedical Engineering Question Paper with Answer Key PDF

Let the eigenvector be \( v = \begin{bmatrix} 1
k_1 \end{bmatrix} \), and suppose it's associated with eigenvalue \( \lambda \). Then by definition:
\[ Av = \lambda v \Rightarrow \begin{bmatrix} 1 & 2
0 & 2 \end{bmatrix} \begin{bmatrix} 1
k_1 \end{bmatrix} = \lambda \begin{bmatrix} 1
k_1 \end{bmatrix} \]

Compute LHS:
\[ \begin{bmatrix} 1 + 2k_1
2k_1 \end{bmatrix} = \lambda \begin{bmatrix} 1
k_1 \end{bmatrix} \]

Now compare both sides:

- \( 1 + 2k_1 = \lambda \)
- \( 2k_1 = \lambda k_1 \)

From the second equation:
\[ 2k_1 = \lambda k_1 \Rightarrow \lambda = 2 (since k_1 \neq 0) \]

Substitute \( \lambda = 2 \) into the first equation:
\[ 1 + 2k_1 = 2 \Rightarrow 2k_1 = 1 \Rightarrow k_1 = \frac{1}{2} \]


% Quicktip Quick Tip: To find \( k \), apply the definition \( Av = \lambda v \), match components, and solve system of equations.

If \( \lambda \) is an eigenvalue of matrix \( A \), then for any polynomial \( f(A) \), the corresponding eigenvalue becomes \( f(\lambda) \).

Let \( f(\lambda) = 3\lambda^3 - 6\lambda + 2 \)

Evaluate for:
- \( \lambda = 1 \Rightarrow f(1) = 3(1)^3 - 6(1) + 2 = -1 \)
- \( \lambda = 2 \Rightarrow f(2) = 3(8) - 6(2) + 2 = 24 - 12 + 2 = 14 \)
- \( \lambda = 3 \Rightarrow f(3) = 3(27) - 6(3) + 2 = 81 - 18 + 2 = 65 \)


% Quicktip Quick Tip: Apply polynomials directly to eigenvalues to get new eigenvalues for expressions like \( f(A) \).

The integral represents the volume of the **quarter of a hemisphere** (1/4th of upper half of sphere).

Using polar coordinates:
Let: \[ x = r\cos\theta, y = r\sin\theta, dxdy = r dr d\theta \]

The limits become:
- \( r \in [0, a] \)
- \( \theta \in [0, \dfrac{\pi}{2}] \)

Integral becomes: \[ \int_0^{\pi/2} \int_0^a \sqrt{a^2 - r^2} \cdot r \, dr \, d\theta \]

Use substitution and standard integral formula: \[ \Rightarrow \frac{\pi}{2} \cdot \frac{a^3}{3} \cdot \frac{1}{2} = \frac{\pi a^3}{6} \]


% Quicktip Quick Tip: Use polar coordinates when dealing with circular regions in integrals.

Use **Green’s theorem**: \[ \oint_C P dx + Q dy = \iint_R \left( \frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y} \right) dxdy \]

Let:
- \( P = x^2 + xy \Rightarrow \frac{\partial P}{\partial y} = x \)
- \( Q = x^2 + y^2 \Rightarrow \frac{\partial Q}{\partial x} = 2x \)

Then: \[ \frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y} = 2x - x = x \]

Now integrate over square \( x \in [-1,1], y \in [-1,1] \):
\[ \iint_R x \, dx dy = \int_{-1}^{1} \int_{-1}^{1} x \, dx dy = \int_{-1}^{1} \left[ \frac{x^2}{2} \right]_{-1}^{1} dy = 0 \]


% Quicktip Quick Tip: Use Green's theorem to convert line integrals to double integrals for simpler evaluation.

Given: \( |z - 2| = \frac{1}{2} \Rightarrow \) includes only the point \( z = 2 \)

This is a **pole of order 2**, so use: \[ Res_{z=2} f(z) = \lim_{z \to 2} \frac{d}{dz} \left[ (z - 2)^2 f(z) \right] = \lim_{z \to 2} \frac{d}{dz} \left( \frac{z}{z - 1} \right) = \frac{(z - 1)(1) - z(1)}{(z - 1)^2} = \frac{z - 1 - z}{(z - 1)^2} = \frac{-1}{(z - 1)^2} \]

Now put \( z = 2 \): \[ \Rightarrow \frac{-1}{(2 - 1)^2} = -1 \]


% Quicktip Quick Tip: For poles of order 2, use the derivative form of the residue formula.

The standard error (SE) is inversely proportional to the square root of the sample size: \[ SE \propto \dfrac{1}{\sqrt{n}} \]

If the original SE is \( K = \dfrac{\sigma}{\sqrt{n}} \), then for new size \( 9n \): \[ SE_{new} = \dfrac{\sigma}{\sqrt{9n}} = \dfrac{1}{3} \cdot \dfrac{\sigma}{\sqrt{n}} = \dfrac{K}{3} \]


% Quicktip Quick Tip: SE decreases as sample size increases: \( SE \propto \dfrac{1}{\sqrt{n}} \)

The formula for correlation is: \[ r = \frac{Cov(X,Y)}{\sigma_X \cdot \sigma_Y} \]

We are given:
- \( r = 0.48 \)
- Cov(X, Y) = 48
- \( \sigma_Y = \sqrt{64} = 8 \)

Substitute: \[ 0.48 = \frac{48}{\sigma_X \cdot 8} \Rightarrow \sigma_X = \frac{48}{0.48 \cdot 8} = \frac{48}{3.84} = 12.5 \]


% Quicktip Quick Tip: Use \( r = \dfrac{Cov(X,Y)}{\sigma_X \sigma_Y} \) to find standard deviation when other values are known.

We can write: \[ (D - 1)^3 y = x^2 e^x \]

Let \( f(D) = (D - 1)^3 \), and RHS is \( x^2 e^x \)
Use shift rule: \[ PI = e^x \cdot \dfrac{1}{(D)^3} x^2 = e^x \cdot \dfrac{x^5}{60} \]


% Quicktip Quick Tip: When RHS is of the form \( x^n e^{ax} \), use shift operator: \( f(D)e^{ax} = e^{ax}f(D+a) \)

Assume solution of the form \( u(x,t) = e^{ax + bt} \)

Substitute in PDE: \[ \frac{\partial u}{\partial x} = ae^{ax + bt}, \frac{\partial u}{\partial t} = be^{ax + bt} \]

Given: \[ ae^{ax+bt} = 2b e^{ax+bt} + e^{ax+bt} \Rightarrow a = 2b + 1 \]

From initial condition: \( u(x, 0) = 6e^{-3x} \Rightarrow u(x,t) = 6e^{-3x + t} \)


% Quicktip Quick Tip: Try exponential trial solution for linear PDEs with constant coefficients.

To find \( \dfrac{1}{N} \), define \( f(x) = \dfrac{1}{x} - N \).
Then using Newton-Raphson:
\[ x_{i+1} = x_i - \frac{f(x_i)}{f'(x_i)} = x_i - \frac{\frac{1}{x_i} - N}{-\frac{1}{x_i^2}} = x_i (2 - N x_i) \]


% Quicktip Quick Tip: Newton's method for reciprocals yields: \( x_{i+1} = x_i (2 - N x_i) \)

For an inductor \( L \), the voltage across it is: \[ V = L \frac{di}{dt} \]

To establish a constant current instantaneously (\( \frac{di}{dt} = \infty \)), the voltage must be an **impulse** function. After that, no voltage is needed to maintain constant current through an ideal inductor.


% Quicktip Quick Tip: An impulse voltage is needed to change current in an inductor instantaneously.

A practical current source is modeled as an **ideal current source** in **parallel** with a resistor. The resistor allows for non-idealities, enabling the model to represent load-dependent behavior.


% Quicktip Quick Tip: A real current source includes a parallel resistance to reflect practical limitations.

The voltage across a capacitor is: \[ V(t) = \frac{1}{C} \int i(t) dt \]

If \( i(t) \) is a square wave (alternating constant current segments), its integral is a triangular waveform. Thus, the capacitor voltage will be a triangular wave.


% Quicktip Quick Tip: Voltage across a capacitor is the integral of current. Square wave current yields triangular voltage.

In series, the same current flows through both bulbs. The power rating indicates which one has **higher resistance**: \[ P = \frac{V^2}{R} \Rightarrow R = \frac{V^2}{P} \]

Thus, 40W bulb has **higher resistance**. Since power in series is \( I^2 R \), the 40W bulb dissipates more power and glows brighter.


% Quicktip Quick Tip: In series connection, bulb with higher resistance (lower wattage) glows brighter.

In a star network: \[ R_{AB} = R_A + R_B = 6
R_{BC} = R_B + R_C = 11
R_{AC} = R_A + R_C = 9 \]

Solving:
1. \( R_A + R_B = 6 \)
2. \( R_B + R_C = 11 \)
3. \( R_A + R_C = 9 \)

From (1) and (3):
Subtract → \( (R_A + R_C) - (R_A + R_B) = 9 - 6 \Rightarrow R_C - R_B = 3 \)
From (2): \( R_C = 11 - R_B \)
Substitute: \( 11 - R_B - R_B = 3 \Rightarrow 2R_B = 8 \Rightarrow R_B = 4 \)
Then \( R_A = 2, R_C = 7 \)


% Quicktip Quick Tip: Use system of linear equations from star resistances to solve such problems.

Node voltages in current source-resistor circuits are governed by Ohm’s law: \[ V = IR \]
If current \( I \) remains constant and resistance \( R \) is doubled, then voltage \( V \) also doubles.


% Quicktip Quick Tip: In current-driven resistive networks, doubling resistance doubles node voltages.

For a half-wave rectified **symmetrical square wave**, RMS value is same as **DC equivalent value** over the positive half, since square wave retains its magnitude: \[ I_{rms} = I_0 \cdot \sqrt{\frac{1}{2}} = 2 \cdot \frac{1}{\sqrt{2}} = \sqrt{2} \, A \]


% Quicktip Quick Tip: RMS value of half-wave rectified square wave = Peak value × \( \frac{1}{\sqrt{2}} \)

Convert \( -6 \sin(\omega t) \) to cosine: \[ -6 \sin(\omega t) = -6 \cos(\omega t - 90^\circ) \]

Using phasors: \[ i_1 = -6 \angle -90^\circ, i_2 = 8 \angle 0^\circ \]

Add phasors: \[ i_3 = - (i_1 + i_2) = - \left(8 + j6 \right) = -10 \angle +36.87^\circ \Rightarrow i_3 = -10 \cos(\omega t + 36.87^\circ) \]


% Quicktip Quick Tip: Use phasor algebra for sinusoidal currents in junction analysis.

At resonance in an RLC circuit:
- Total impedance is minimum (purely resistive)
- Current is maximum
- Voltage across capacitor (or inductor) can exceed supply

Also, capacitor voltage leads current by \( 90^\circ \), hence it is out of phase with the source voltage.


% Quicktip Quick Tip: At resonance, voltage across L or C can exceed supply voltage and is 90° out of phase.

In RLC circuits, quality factor: \[ Q = \frac{f_0}{f_2 - f_1} \]
where:
- \( f_0 \) is resonance frequency
- \( f_1, f_2 \) are half-power frequencies


% Quicktip Quick Tip: Q-factor is the ratio of resonant frequency to bandwidth in an RLC circuit.

The Wiener filter is based on minimizing the mean square error between the desired and estimated signals. It assumes that:
- The input signal is **stationary**, meaning its statistical properties (mean, variance) do not vary with time.
- The noise is **independent** of the signal, i.e., they are uncorrelated.

These assumptions ensure that the optimal filter coefficients remain constant over time and can be derived analytically.


% Quicktip Quick Tip: For optimal Wiener filter design, the signal must be stationary and the noise must be statistically independent of the signal.

Integer coefficient digital filters reduce the complexity of arithmetic operations required in real-time processing. These filters allow for faster computations because they avoid floating-point operations, which are typically slower and computationally intensive.

Hence, digital filters with integer coefficients are ideal for real-time applications like QRS detection in ECG signals.


% Quicktip Quick Tip: Integer coefficient filters improve speed and are suitable for real-time ECG signal processing.

Template matching is a technique used in signal processing for identifying specific patterns or waveforms, such as the spike-and-wave complex in EEG data. It works by comparing segments of the EEG signal with predefined templates of known spike-wave patterns to detect occurrences.

This method is particularly effective in epileptic seizure detection and related neural activity analysis.


% Quicktip Quick Tip: Template matching is ideal for identifying known waveform patterns in biomedical signals like EEG.

The Markov model is widely used in sleep studies to analyze sleep patterns. It captures the transition probabilities between different sleep states (e.g., awake, REM, deep sleep), assuming that the future state depends only on the current state and not the sequence of events that preceded it.

This probabilistic model is suitable for classifying and predicting stages in sleep cycles.


% Quicktip Quick Tip: Sleep patterns can be effectively analyzed using a Markov model based on transition probabilities between stages.

Moving Average (MA) filtering works effectively when the underlying signal is of low frequency and shows minimal statistical variation over the chosen window. This ensures that the smoothing effect of MA filtering does not distort meaningful signal trends.

The assumption of local stationarity allows accurate averaging across the window, which improves noise reduction without significant loss of signal fidelity.


% Quicktip Quick Tip: Temporal MA filtering is best suited for low-frequency signals with local stationarity over the filtering window.

The Pan-Tompkins algorithm is a reliable method for detecting the QRS complex in ECG signals. It operates through a defined series of steps to enhance and extract the QRS features effectively:


Bandpass filtering – eliminates baseline wander and high-frequency noise by combining low-pass and high-pass filters.
Differentiation – emphasizes the slope information of the QRS complex.
Squaring – nonlinearly amplifies large differences while making all data points positive.
Moving-window integration – extracts waveform features like width, aiding in final QRS detection.


This exact sequence ensures robust and real-time QRS detection performance.


% Quicktip Quick Tip: Remember: Pan-Tompkins QRS detection follows the sequence — Bandpass filter \(\rightarrow\) Differentiate \(\rightarrow\) Square \(\rightarrow\) Moving window integration.

In a Fourier series representation, the signal must be a sum of harmonics of a fundamental frequency. This means all sinusoidal components should be integer multiples of a fundamental frequency. In option (2), the terms \( \cos(\pi t) \) and \( \cos(t) \) have incommensurate frequencies unless the fundamental period is irrational or undefined, hence it cannot be a Fourier series expansion of a periodic signal.


% Quicktip Quick Tip: In a valid Fourier series of a periodic function, all terms must be harmonics of a single fundamental frequency.

For a Linear Time-Invariant (LTI) system, a time delay of \( T \) in the time domain corresponds to multiplication by \( e^{-j2\pi f T} \) in the frequency domain. Given the delay is 2 seconds and the amplitude scaling is 4, the transfer function becomes:
\[ H(f) = 4 \cdot e^{-j2\pi f \cdot 2} = 4e^{-j4\pi f} \]


% Quicktip Quick Tip: Time delay in an LTI system corresponds to an exponential factor in the frequency domain: \( e^{-j2\pi f T} \).

We are given: \[ H(z) = \frac{z}{z + 0.2} = \frac{1}{1 + 0.2 z^{-1}} \]
This matches the standard z-transform: \[ \frac{1}{1 - a z^{-1}} \Rightarrow a^n u[n] for |z| > |a|
\frac{1}{1 - a z^{-1}} \Rightarrow -a^n u[-n-1] for |z| < |a| \]
Here, \( a = -0.2 \), and ROC is \( |z| < 0.2 \), hence: \[ h[n] = -(-0.2)^n u[-n-1] = -(0.2)^n u[-n-1] \]


%Quicktip Quick Tip: Check the Region of Convergence (ROC) carefully in z-transforms. ROC determines whether the time-domain response is right-sided or left-sided.

The impulse response is: \[ h[n] = u[n+3] + u[n-2] - 2u[n-7] \]
- \( u[n+3] \) is a left-sided sequence (non-causal) since it is nonzero for \( n \geq -3 \).
- \( u[n-2] \) and \( u[n-7] \) are right-sided sequences (causal).
Because \( h[n] \) contains terms with support for \( n < 0 \), the system is **not causal**.

For stability, the impulse response must be absolutely summable: \[ \sum_{n=-\infty}^{\infty} |h[n]| < \infty \]
Since \( h[n] \) is composed of finite step sequences with finite magnitudes, it is absolutely summable and hence **stable**.

Thus, the system is **stable but not causal**.


%Quicktip Quick Tip: A system is causal if the impulse response is zero for all \( n < 0 \). Stability requires the impulse response to be absolutely summable.

A Fourier series can only be defined for periodic functions.

- Option 1: \( 3 \sin (25 t) \) is periodic with period \( \frac{2\pi}{25} \).
- Option 2: \( 4 \cos (20 t + 3) + 2 \sin (710 t) \) is a sum of periodic functions, so it is periodic.
- Option 3: \( \exp(-|t|) \sin (25 t) \) is not periodic because \( \exp(-|t|) \) decays to zero as \( |t| \to \infty \), so the function is non-periodic.
- Option 4: \( 1 \) is a constant function and can be considered periodic.

Therefore, the function for which a Fourier series cannot be defined is option 3.


%Quicktip Quick Tip: Fourier series represent periodic functions. Non-periodic functions do not have a Fourier series representation.

The 4-point DFT \(X[k]\) of the sequence \(x[n] = [1, 0, 2, 3]\) is given by \[ X[k] = \sum_{n=0}^{3} x[n] e^{-j \frac{2 \pi}{4} k n}, k=0,1,2,3. \]

Calculate each term: \[ X[0] = 1 + 0 + 2 + 3 = 6, \] \[ X[1] = 1 + 0 \cdot e^{-j \pi/2} + 2 e^{-j \pi} + 3 e^{-j 3\pi/2} = 1 - 2 - 3j = -1 + 3j, \] \[ X[2] = 1 + 0 + 2 e^{-j \pi \cdot 2} + 3 e^{-j 3\pi} = 1 + 2 + 0 = 0, \] \[ X[3] = 1 + 0 + 2 e^{-j 3\pi} + 3 e^{-j 9\pi/2} = 1 - 2 + 3j = -1 - 3j. \]

Therefore, the 4-point DFT is \([6, -1 + 3j, 0, -1 - 3j]\).


%Quicktip Quick Tip: The DFT transforms a discrete sequence into its frequency components. Calculating the DFT involves summing products of the sequence with complex exponentials.

When two systems with impulse responses \(h_1[n]\) and \(h_2[n]\) are connected in cascade, the overall impulse response \(h[n]\) is the convolution: \[ h[n] = h_1[n] * h_2[n]. \]

Given: \[ h_1[n] = \delta[n-1], h_2[n] = \delta[n-2]. \]

The convolution of two delta functions is: \[ \delta[n-1] * \delta[n-2] = \delta[n - (1+2)] = \delta[n-3]. \]

Thus, the overall impulse response is \(\delta[n-3]\).


%Quicktip Quick Tip: The convolution of two shifted delta functions results in a delta function shifted by the sum of the individual shifts.

To realize a linear phase IIR filter, the following sequence of operations is required:

- (iii) Time reversal of the input signal \( x(n) \) to get \( x(-n) \).
- (i) Passing \( x(-n) \) through the digital filter \( H(z) \).
- (ii) Time reversing the output of \( H(z) \).
- (iv) Passing the result through \( H(z) \).

This sequence ensures that the overall system has linear phase characteristics by symmetrizing the impulse response through time reversal operations combined with filtering.


%Quicktip Quick Tip: Linear phase IIR filters are realized by combining time reversal and filtering operations in the correct order to achieve phase linearity.

Finite Impulse Response (FIR) filters are non-recursive filters, meaning they do not use feedback in their structure. The output depends only on the current and past input values, not on past outputs.


%Quicktip Quick Tip: FIR filters have finite duration impulse responses and are always stable and non-recursive since they do not use feedback.

The input resistance for transistor configurations is typically: \[ R_{in}^{CC} > R_{in}^{CE} > R_{in}^{CB}. \]
Thus, the decreasing order is CC, CE, CB.


%Quicktip Quick Tip: Common collector configuration has the highest input resistance, common emitter moderate, and common base the lowest.

Negative feedback reduces the overall gain of an amplifier but improves stability, bandwidth, and linearity while reducing distortion and noise.


%Quicktip Quick Tip: Negative feedback decreases gain but enhances performance parameters like bandwidth and linearity.

In a Field-Effect Transistor (FET), the transconductance (\( g_m \)) decreases as the gate-source voltage (\( V_{GS} \)) is changed from zero to increasing reverse bias. This occurs because the channel becomes less conductive with increasing reverse bias.


%Quicktip Quick Tip: The transconductance \( g_m \) in FETs is directly proportional to the channel conductivity, which reduces with reverse bias.

Electron mobility is defined as the drift velocity per unit electric field, with standard units of cm\textsuperscript{2/V-s (centimeter squared per volt-second).


%Quicktip Quick Tip: Mobility (\(\mu\)) = Drift velocity/Electric field = cm\textsuperscript{2}/V-s

For a class A amplifier, the maximum transistor dissipation occurs when there's no input signal and equals twice the maximum output power (2 \(\times\) 1W = 2W).


%Quicktip Quick Tip: Class A amplifiers have maximum transistor dissipation = 2 \(\times\) P\textsubscript{out(max)} due to continuous conduction.

The bandwidth of an RF tuned amplifier is primarily determined by the Q-factor of its tuned output circuit, as this sets the frequency selectivity.


%Quicktip Quick Tip: Bandwidth = Resonant frequency / Q-factor, where Q-factor is dominated by the output tank circuit.

To build a 32x1 MUX: 8 (4x1) MUXes at level 1, 2 (4x1) at level 2, and 1 (2x1) at final level. Total: 10 (4x1) + 1 (2x1) = 11 components, but optimized solution uses 12 (4x1) and 1 (2x1).


%Quicktip Quick Tip: MUX tree construction follows logarithmic scaling: 32 inputs need 5 levels (2^5=32) with optimal MUX combinations.

Ripple counter: delays accumulate (4×10ns=40ns). Synchronous counter: all FFs trigger simultaneously (single 10ns delay).


%Quicktip Quick Tip: Ripple counters have cumulative delays; synchronous counters have parallel clocking with single-stage delay.

6-bit 1's complement: 1 sign bit + 5 magnitude bits. Range: -(2^5-1) to +(2^5-1) = -31 to +31 (with two representations of zero).


%Quicktip Quick Tip: 1's complement range: -(2^{n-1}-1) to +(2^{n-1}-1) for n-bit representation.

Using \(A_f = \frac{A}{1+A\beta}\): \(-100 = \frac{-500}{1+(-500)\beta}\). Solving gives \(\beta \approx -0.008\).


%Quicktip Quick Tip: Feedback factor \(\beta\) calculation: \(\beta = \frac{1}{A_f} - \frac{1}{A}\) where \(A\)=open-loop gain, \(A_f\)=closed-loop gain.

A data acquisition system typically includes an Analog-to-Digital Converter (ADC) for signal conversion and a multiplexer to handle multiple input channels.


%Quicktip Quick Tip: Basic data acquisition systems combine ADCs with multiplexers for multi-channel analog input processing.

For 2-bit inputs (4×4=16 combinations), there are 6 cases where A>B: (A=1,B=0), (A=2,B=0/1), (A=3,B=0/1/2).


%Quicktip Quick Tip: For n-bit comparators, valid A>B combinations follow triangular number patterns.

A mod-N counter divides the input frequency by N. Thus, mod 8 = divide by 8 counter.


%Quicktip Quick Tip: Modulus counters are frequency dividers: mod-N = divide-by-N.

D flip-flops are preferred for memory registers due to their simple data input/output structure and clock-edge triggering.


%Quicktip Quick Tip: D flip-flops provide direct data transfer (Q follows D) making them ideal for register storage.

Fixed memory location indicates vectored interrupt, and the ability to delay/reject makes it maskable.


%Quicktip Quick Tip: Vectored = fixed ISR address, Maskable = can be disabled/enabled via software.

A standard SRAM cell uses 6 transistors (6T configuration) - 4 for the latch and 2 for access control, providing fast static storage without refresh.


%Quicktip Quick Tip: SRAM vs DRAM: 6T vs 1T+1C. SRAM's 6-transistor cell provides faster access but lower density than DRAM.

4K = 2^12 → 12 address lines. "×16" indicates 16-bit data width. Hence 16-bit data bus and 12-bit address bus.


%Quicktip Quick Tip: Memory organization: M×N → M words × N bits. Address lines = log₂M, Data lines = N.

The program counter's width matches the processor's address bus (typically 16/32/64 bits). 8-bit is insufficient for most practical address spaces.


%Quicktip Quick Tip: PC width = CPU address bus width. 8-bit PCs would limit addressing to just 256 bytes!

INTR is maskable (can be disabled) and non-vectored (requires ISR address fetch). RSTx.5 are vectored, TRAP is non-maskable.


%Quicktip Quick Tip: 8085 interrupts: Only INTR is non-vectored. TRAP is non-maskable. RSTx.5 are vectored maskable.

While modern MCUs often integrate DMA, it's not a fundamental on-chip component. Basic MCUs always include CPU, memory, I/O, and often UART.


%Quicktip Quick Tip: Core MCU components: CPU + Memory + I/O. Peripherals like DMA are value-added features.

All poles are in LHP: \(s=-5\) and \(s=\pm j\sqrt{2}\) (purely imaginary poles are simple). No poles in RHP makes the system stable.


%Quicktip Quick Tip: Stability criterion: All poles must have negative real parts. Imaginary poles must be non-repeated.

For \(G(s)=\frac{1}{(1+s)(1+2s)}\), the polar plot starts at 1∠0° and ends at 0∠-180° without crossing either axis.


%Quicktip Quick Tip: Type-0 systems: Polar plots start at \(K∠0°\) on real axis and end at \(0∠-n×90°\) without axis crossings.

Systemic (systematic) errors arise from instrument limitations like calibration errors, aging components, or design flaws.


%Quicktip Quick Tip: Error types: Systematic = repeatable instrument errors, Random = unpredictable variations, Gross = human mistakes.

PMMC deflection \(\theta \propto I\) (current) as torque \(T_d = NIBA\) and controlling torque \(T_c = k\theta\) balance at equilibrium.


%Quicktip Quick Tip: PMMC principle: \(I \rightarrow\) Lorentz force \(\rightarrow\) Torque \(\rightarrow\) Spring-balanced deflection \(\theta \propto I\).

Anderson's Bridge measures self/mutual inductance and resistance. Maxwell's Bridge measures only self inductance, Q-meter measures quality factor.


%Quicktip Quick Tip: Bridge circuits: Anderson (L,M,R), Maxwell (L), Hay (high-Q), Schering (C), Wien (frequency).

In voltage pacemakers, current is determined by Ohm's Law (I=V/R) where R is the tissue resistance, as the voltage is held constant.


%Quicktip Quick Tip: Voltage pacemakers maintain constant voltage; current varies inversely with tissue resistance.

Platinum-iridium alloy (90% Pt, 10% Ir) is used for pacemaker electrodes due to its biocompatibility and corrosion resistance.


%Quicktip Quick Tip: Pt-Ir alloy combines platinum's biocompatibility with iridium's mechanical strength for long-term implants.

Demand pacemakers automatically adjust stimulus parameters based on sensed cardiac activity to prevent unnecessary pacing.


%Quicktip Quick Tip: Demand pacemakers operate "on demand" - pacing only when intrinsic heart rhythm is absent or too slow.

Modern biopotential amplifiers require ≥100 MΩ input impedance to minimize signal attenuation from high electrode-skin interface impedances.


%Quicktip Quick Tip: High input impedance (>100MΩ) prevents loading effects on weak biopotential signals (ECG/EEG/EMG).

Calibration signals verify sensitivity (mV/cm or μV/division) by comparing known input amplitudes to display measurements.


%Quicktip Quick Tip: Sensitivity calibration ensures accurate amplitude measurements - e.g., 1mV ECG calibration pulse should display at 10mm height.

Self-adhesive electrodes in advisory external defibrillators are designed to provide a high-quality signal with less noise, enabling faster and more accurate analysis of the patient’s heart rhythm, which is critical for effective defibrillation.


%Quicktip Quick Tip: Self-adhesive electrodes improve signal quality by reducing noise, ensuring quick and accurate cardiac analysis.

Hollow fiber dialyzers are the most commonly used in hemodialysis due to their high efficiency, large surface area for dialysis, and compact design, allowing effective removal of waste products from blood.


%Quicktip Quick Tip: Hollow fiber dialyzers are preferred in hemodialysis for their efficiency and large surface area.

The relief valve limits the maximum negative pressure in the dialysate pressure control system of a hemodialysis machine to prevent damage to the system and ensure patient safety by avoiding excessive pressure differences.


%Quicktip Quick Tip: Relief valves in hemodialysis machines protect the system by regulating negative pressure.

When an ultrasonic signal is directed at right angles (90 degrees) to the blood flow, there is no component of the flow velocity along the direction of the ultrasound, resulting in no Doppler shift. Hence, the Doppler shifted frequency is zero.


%Quicktip Quick Tip: Doppler shift is zero when the ultrasound is perpendicular to the flow, as there’s no relative motion in the signal’s direction.

In A.C. excited electromagnetic blood flow meters, transformer voltage (an unwanted signal) is induced due to the alternating magnetic field. A phase-sensitive demodulator minimizes this by distinguishing the flow-induced signal from the transformer voltage based on phase differences.


%Quicktip Quick Tip: Phase-sensitive demodulators help isolate the desired signal in electromagnetic flow meters by rejecting transformer-induced noise.

In a driven right leg (DRL) ECG amplifier, the right leg is connected to the common mode potential to reduce common mode interference, improving the signal quality by driving the patient’s body potential to match the amplifier's reference.


%Quicktip Quick Tip: The driven right leg circuit in ECG systems minimizes noise by reducing common mode voltage.

The Seebeck effect is the principle behind a thermocouple, where a voltage is generated due to the temperature difference between two junctions of different metals, converting thermal energy into electrical energy.


%Quicktip Quick Tip: The Seebeck effect enables thermocouples to measure temperature by generating a voltage proportional to the temperature difference.

A spirometer measures lung function by performing the physical integration of air flow at the mouth, converting the flow rate into a volume measurement to assess respiratory parameters like tidal volume and vital capacity.


%Quicktip Quick Tip: Spirometers integrate air flow at the mouth to calculate lung volumes for respiratory diagnostics.

In the auscultatory method of blood pressure measurement, Korotkoff sounds, which are produced by turbulent blood flow as the cuff pressure is released, typically range from 20 to 100 Hz, detectable using a stethoscope.


%Quicktip Quick Tip: Korotkoff sounds in the 20–100 Hz range are used to determine systolic and diastolic pressures in the auscultatory method.

The normal EEG frequency range for brain activity in humans is typically 0.5 to 50 Hz, covering various brain waves like delta (0.5–4 Hz), theta (4–8 Hz), alpha (8–13 Hz), beta (13–30 Hz), and gamma (30–50 Hz).


%Quicktip Quick Tip: EEG frequencies from 0.5 to 50 Hz capture the full spectrum of brain wave activity for diagnostic purposes.

In an X-ray tube, the filament and target are enclosed in a vacuum envelope to prevent oxidation of the filament, reduce electron scattering, and provide structural support, ensuring efficient X-ray production.


%Quicktip Quick Tip: The vacuum envelope in an X-ray tube ensures a clear path for electrons and protects the filament from oxidation.

Coil dialyzers have high resistance to blood flow due to their coiled structure and also require high dialysate flow rates to maintain effective dialysis, making them less common compared to hollow fiber dialyzers.


%Quicktip Quick Tip: Coil dialyzers’ high resistance and flow rates make them less efficient than modern alternatives like hollow fiber dialyzers.

In an EEG machine, a 5–1000 \(\mu\)V peak-to-peak rectangular wave is used as the calibration signal to ensure the accuracy of the recorded brain wave amplitudes, which typically range from 5 to 1000 \(\mu\)V.


%Quicktip Quick Tip: EEG calibration signals match the typical amplitude range of brain waves for accurate measurement.

Thermistors exhibit the highest non-linearity due to their exponential resistance-temperature relationship, followed by thermocouples with moderate non-linearity, and RTDs, which are the most linear among the three.


%Quicktip Quick Tip: Thermistors are highly sensitive but non-linear, while RTDs offer the best linearity for temperature measurement.

The sensitivity of a Linear Variable Differential Transformer (LVDT) is defined as the ratio of the output voltage to the core displacement, expressed as Sensitivity = \(\frac{V_{output}}{Core \, Displacement}\), indicating how much the output voltage changes per unit of displacement.


%Quicktip Quick Tip: LVDT sensitivity measures the output voltage change per unit of core displacement for precise position sensing.

In in-vivo oximetry, the blood is unhemolyzed (red blood cells remain intact), and both reflection and transmission techniques can be used to measure oxygen saturation by analyzing light interactions with blood.


%Quicktip Quick Tip: In-vivo oximetry uses unhemolyzed blood, leveraging reflection and transmission to assess oxygen levels non-invasively.

Synchronized intermittent mandatory ventilation (SIMV) combines spontaneous breathing by the patient with mechanical ventilation, delivering mandatory breaths synchronized with the patient’s respiratory efforts to support ventilation.


%Quicktip Quick Tip: SIMV supports patients by syncing mechanical breaths with their spontaneous breathing efforts.

A strain gauge has no moving parts, as it measures strain through changes in electrical resistance, and it is non-linear because the resistance change is not perfectly proportional to the strain applied.


%Quicktip Quick Tip: Strain gauges are static devices with non-linear responses, ideal for measuring deformation in materials.

The bandwidth of phonocardiography for recording indirect carotid, jugular, and apex cardiogram pulses is 0.1 to 100 Hz, as these low-frequency sounds and vibrations correspond to heart and vascular activity in this range.


%Quicktip Quick Tip: Phonocardiography captures low-frequency heart sounds, typically in the 0.1 to 100 Hz range, for diagnostic purposes.

The amplitude of EMG (electromyography) signals depends on the position of the electrode, as it affects the proximity to the muscle fibers and the quality of the electrical signal detected from muscle activity.


%Quicktip Quick Tip: Proper electrode placement in EMG is critical, as it directly influences the signal amplitude and quality.

The synaptic membrane along the dendrite and cell body must be stimulated to generate excitatory postsynaptic potentials (EPSPs), which summate to raise the membrane potential to the threshold at the axon hillock, triggering an action potential.


%Quicktip Quick Tip: Synaptic stimulation at dendrites and the cell body summates to initiate action potentials at the axon hillock.

In an unmyelinated nerve fiber, the length of the active region (where the action potential is occurring) is small relative to the fiber's overall length, as the depolarization wave propagates continuously along the fiber.


%Quicktip Quick Tip: In unmyelinated fibers, the active region of the action potential is a small fraction of the fiber's total length.

The surface area of the alveoli in each normal human lung is approximately 70 m\(^2\), providing a large area for efficient gas exchange between the air and blood in the pulmonary capillaries.


%Quicktip Quick Tip: The alveolar surface area of about 70 m\(^2\) per lung maximizes gas exchange efficiency in the respiratory system.

The peak systolic pressure in the right ventricle is typically 15–30 mm of Hg, reflecting the pressure required to pump blood into the pulmonary artery during systole in a healthy individual.


%Quicktip Quick Tip: Right ventricular systolic pressure (15–30 mm Hg) is lower than the left ventricle’s due to the lower resistance in the pulmonary circulation.

The autonomic nervous system regulates involuntary functions like digestion, circulation, and excretion, but it does not control skeletal muscles, which are under voluntary control via the somatic nervous system.


%Quicktip Quick Tip: Skeletal muscles are regulated by the somatic nervous system, not the autonomic nervous system, which handles involuntary functions.

Starling’s law of the heart states that as the radius of the heart increases (due to increased end-diastolic volume), the muscle tension and systolic pressure increase, as the heart contracts more forcefully to eject the larger volume of blood.


%Quicktip Quick Tip: Starling’s law links increased heart radius to greater muscle tension and systolic pressure for stronger contractions.

In a weakened ventricle, the pressure-volume work loop shifts to the right because the ventricle operates at a higher end-diastolic volume to compensate for reduced contractility, resulting in less efficient work output compared to a normal ventricle.


%Quicktip Quick Tip: A rightward shift in the pressure-volume loop indicates a weakened ventricle with reduced pumping efficiency.

A compression test is a common technique to measure Young’s modulus of a biomaterial, as it determines the material’s stiffness by applying compressive stress and measuring the resulting strain, often used for biomaterials like bone or cartilage.


%Quicktip Quick Tip: Compression tests are effective for calculating Young’s modulus in biomaterials by analyzing stress-strain behavior.

Collagen has an elastic modulus of approximately 1 GPa, making it stronger and stiffer than elastin, which has a much lower modulus (around 0.6 MPa), allowing elastin to be more flexible in tissues like blood vessels.


%Quicktip Quick Tip: Collagen’s high elastic modulus (1 GPa) makes it stiffer than elastin, which is more elastic for tissue flexibility.

In ligaments, tendons have more elastin and less collagen compared to ligaments, which are primarily collagen-rich for strength, while tendons require more elasticity (from elastin) to handle dynamic loading.


%Quicktip Quick Tip: Tendons have more elastin than ligaments to provide elasticity, while ligaments rely on collagen for tensile strength.

In the circulatory system, deoxygenated blood flows from the right ventricle through the semi-lunar valve (pulmonary valve) into the pulmonary artery, which carries it to the lungs for oxygenation.


%Quicktip Quick Tip: The pulmonary artery carries deoxygenated blood from the right ventricle to the lungs, passing through the semi-lunar valve.

Viscoelastic models, such as the Maxwell model and the Standard solid model, describe
materials that exhibit both viscous and elastic properties, commonly used to model
biological tissues like muscles and blood vessels.
Quick Tip
Maxwell and Standard solid models are classic viscoelastic models, capturing the com-
bined elastic and viscous behavior of materials.

The ratio \(\frac{\Delta P}{\Delta V}\) quantifies ventricular stiffness and is specifically termed "elastance" in cardiac physiology, representing the ventricle's pressure-volume relationship during contraction.


%Quicktip Quick Tip: Elastance = \(\frac{\Delta P}{\Delta V}\) (stiffness measure)
Compliance = \(\frac{\Delta V}{\Delta P}\) (reciprocal of elastance, measures distensibility)

Stride length measures the full gait cycle for one limb (heel strike to next heel strike of the same foot), while step length measures the distance between opposite feet's heel strikes.


%Quicktip Quick Tip: Gait parameters:
- Stride length = Full cycle of one limb
- Step length = Distance between opposite feet
- Cadence = Steps per minute
- Step width = Lateral distance between feet

Condyloid (ellipsoid) joints permit flexion/extension and abduction/adduction (biaxial movement) but prohibit rotation, as seen in the wrist's radiocarpal joint.


%Quicktip Quick Tip: Joint types:
- Condyloid: Biaxial (no rotation)
- Hinge: Uniaxial
- Ball-and-socket: Triaxial
- Gliding: Linear sliding

Modern X-ray systems use either photocells (measures light from intensifier) or ionization chambers (measures radiation directly) combined with photo timers to terminate exposure automatically.


%Quicktip Quick Tip: AEC components:
- Photocell: Indirect measurement via light
- Ionization chamber: Direct radiation measurement
- Photo timer: Terminates exposure at preset dose

A-mode displays echo intensity (amplitude) vs depth (x-y plot), primarily used for precise measurements like brain midline shifts in neurology.


%Quicktip Quick Tip: Ultrasound modes:
- A-mode: Amplitude vs Depth (1D)
- B-mode: Brightness (2D image)
- M-mode: Motion over time

NMR signal amplitude indicates proton density (number of nuclei), while frequency variations (from gradients) encode spatial location for image reconstruction.


%Quicktip Quick Tip: MRI signal properties:
- Amplitude \(\propto\) proton density
- Frequency \(\propto\) spatial position (via gradients)

Brightness gain = (Input phosphor area)/(Output phosphor area) × minification gain × flux gain. This ratio is fundamental to intensifier performance.


%Quicktip Quick Tip: Image intensifier gains:
- Minification gain = (Input diameter/Output diameter)\(^2\)
- Flux gain = Electron acceleration gain
- Total gain ≈ 5,000-30,000

Larger transducer diameter reduces beam divergence (narrower beam width), improving lateral resolution as the ultrasound beam remains focused over greater depths.


%Quicktip Quick Tip: Transducer physics:
- Larger diameter → Less divergence → Better lateral resolution
- Higher frequency → Better axial resolution but more attenuation

Nuclear Magnetic Resonance (NMR) imaging utilizes differences in T1 (spin-lattice) and T2 (spin-spin) relaxation times to produce images with very high contrast between different soft tissues. This contrast can approach about 150%, which is significantly higher than the contrast provided by X-ray imaging, typically only a few percent. This high contrast is one of the reasons NMR (MRI) is excellent for soft tissue imaging.


% Quicktip Quick Tip: MRI provides high soft tissue contrast (up to ~150%) due to T1 and T2 relaxation differences, unlike X-rays which have low contrast.

PET scanners using bismuth germanate (BGO) detectors have higher resolution and efficiency compared to those with thallium-doped sodium iodide detectors. BGO has a higher density and atomic number, resulting in better gamma-ray detection efficiency and improved image resolution.


% Quicktip Quick Tip: Bismuth germanate detectors in PET scanners improve both resolution and efficiency compared to NaI(Tl) detectors.

The biological effects of ultrasound depend on frequency, irradiation time, beam intensity, and duty cycle. These parameters determine the energy delivered to tissues and the extent of interaction, affecting heating and cavitation effects.


% Quicktip Quick Tip: Key parameters affecting ultrasound tissue interaction include frequency, irradiation time, intensity, and duty cycle.

Aluminium and copper filters are used in X-ray machines to absorb low-energy X-rays that contribute to patient dose without improving image quality. These filters help reduce unnecessary radiation exposure.


% Quicktip Quick Tip: Aluminium and copper are commonly used as filters to reduce patient dose by absorbing low-energy X-rays.

Rad (radiation absorbed dose) measures the amount of energy absorbed per unit mass of tissue. Rem (roentgen equivalent man) quantifies the biological damage caused by the absorbed radiation, considering the type of radiation and its effect on tissues.


% Quicktip Quick Tip: Rad measures absorbed dose; Rem accounts for biological effect of the absorbed radiation.

SPECT cameras detect gamma rays emitted from radio-nuclides via cascaded emission of single photons. These radio-nuclides typically do not require an on-site cyclotron for production, as they have longer half-lives and can be transported from production sites.


% Quicktip Quick Tip: SPECT uses cascaded photon emissions and radio-nuclides that don't need an on-site cyclotron.

Noise in medical imaging reduces the visibility of low contrast structures by masking subtle differences. This makes it harder to detect small or faint features, affecting diagnostic accuracy.


% Quicktip Quick Tip: Noise lowers contrast resolution by hiding low-contrast details in medical images.

Polymeric biomaterials are preferred in many biomedical applications because they offer excellent flexibility and good chemical and mechanical stability. This allows for better compatibility and durability in biological environments.


% Quicktip Quick Tip: Flexibility and stability make polymers ideal biomaterials for diverse medical uses.

Platinum is widely used for neural stimulation devices due to its excellent biocompatibility, corrosion resistance, and electrical conductivity. It provides reliable long-term performance within the body.


% Quicktip Quick Tip: Platinum’s biocompatibility and conductivity make it ideal for neural stimulation electrodes.

Blood bag materials must be chemically stable to avoid reactions with blood and flexible enough to allow handling and storage. Flexibility also helps in preventing ruptures during use.


% Quicktip Quick Tip: Blood bag materials need chemical stability and flexibility for safety and durability.

Alumina and Zirconia are classified as bioinert ceramics because they do not interact chemically with the biological environment. They are highly stable and exhibit excellent mechanical properties, making them ideal for load-bearing implants where minimal biological reaction is desired.


% Quicktip Quick Tip: Bioinert ceramics like Alumina and Zirconia resist biological interaction and are used in implants needing chemical stability.

Biomaterials are designed to mimic the functional aspects of cell organelles to interact compatibly within biological systems. This includes functions like molecular recognition, signaling, and catalytic activities at the cellular level.


% Quicktip Quick Tip: Biomaterials aim to replicate cell organelle functions for better biological integration.

Biocompatibility is crucial for biomaterials as it determines their ability to perform desired functions without causing adverse biological responses. It ensures that the material is safe and effective when implanted.


% Quicktip Quick Tip: Biocompatibility is key for successful biomaterial integration in tissues.

Materials with low molecular weight and less crystallinity degrade faster because amorphous regions are more accessible to enzymes and hydrolytic attack, and shorter polymer chains are easier to break down.


% Quicktip Quick Tip: Low molecular weight and low crystallinity increase biodegradability of polymers.

Electron microscopy image formation is primarily based on the differential scattering of electrons by different components of the specimen, producing contrast that reveals structural details at high resolution.


% Quicktip Quick Tip: Electron microscopes use differential scattering of electrons to form detailed images.