GATE EC flashcards

33 cards. Read the term and the definition here. The deck at the top of this page is optional.

Transconductance gm of BJT

gm = IC/VT, where VT is the thermal voltage, about 26 mV at room temperature. It equals the slope of the collector-current versus base-emitter-voltage curve at the bias point.

Early effect

Base-width modulation by the collector-base reverse bias causes IC to rise slightly with VCE in the active region. It is modeled by the Early voltage VA, giving output resistance ro = VA/IC.

MOSFET triode condition

The device is in the linear (triode) region when VDS < VGS − VTH. There the channel is continuous and ID ≈ μnCox(W/L)[(VGS − VTH)VDS − VDS²/2].

Body effect

A nonzero source-to-body reverse bias increases threshold voltage according to VTH = VTH0 + γ(√(2φF + VSB) − √(2φF)). The parameter γ is the body-effect coefficient.

Virtual ground

With ideal negative feedback and infinite gain, the op-amp drives V− to equal V+. The input node sits at a fixed potential without being physically grounded, so current flows through feedback.

Slew rate

Maximum rate of change of the op-amp output, usually given in V/μs. It limits large-signal response at high frequency; full-power bandwidth equals slew rate divided by 2π times peak amplitude.

CMRR

Common-mode rejection ratio is the differential gain divided by the common-mode gain, often expressed in decibels. It quantifies how well a differential amplifier rejects signals present on both inputs.

Barkhausen criterion

For sustained sinusoidal oscillation, the loop gain must have magnitude one and phase shift of zero or a multiple of 360 degrees at the oscillation frequency. Excess gain causes amplitude growth into nonlinear limiting.

Routh-Hurwitz criterion

Build the Routh array from the characteristic polynomial coefficients. The number of sign changes in the first column equals the number of closed-loop poles in the right half-plane.

Phase margin

Phase margin is 180 degrees plus the open-loop phase at the gain-crossover frequency where magnitude equals one. It measures relative stability; roughly 45 to 60 degrees is a typical design target.

Steady-state error

For a unity-feedback system, steady-state error depends on system type and input. Step input needs a type-1 loop for zero error; ramp input needs type 2; acceleration input needs type 3.

PID controller

A controller with proportional, integral, and derivative terms: Gc(s) = Kp + Ki/s + Kd s. Integral action removes steady-state error; derivative action adds damping and improves transient response.

Nyquist sampling theorem

A signal strictly bandlimited to fm hertz can be reconstructed exactly from samples taken at fs > 2fm. Sampling at or below 2fm causes spectral overlap called aliasing.

Z-transform ROC

The region of convergence is the set of z values where the z-transform sum converges. For a right-sided sequence it lies outside the outermost pole; for a left-sided sequence it lies inside the innermost pole.

Final value theorem

For a stable system, the steady-state value equals lim(s→0) sX(s), provided all poles of sX(s) lie in the left half-plane. It converts a Laplace-domain expression directly to a time-domain limit.

Parseval's theorem

Total energy computed in the time domain equals total energy computed in the frequency domain. For a Fourier transform pair, ∫|x(t)|²dt = ∫|X(f)|²df.

Convolution theorem

Convolution in the time domain corresponds to multiplication of Fourier transforms, and multiplication in time corresponds to convolution in frequency. It underlies LTI system analysis via transfer functions.

DFT length and resolution

An N-point DFT of a signal sampled at fs gives frequency bins spaced fs/N hertz apart. Zero-padding interpolates the spectrum but does not improve true frequency resolution, which depends on observation time.

Group delay

Group delay is the negative derivative of phase with respect to angular frequency. Constant group delay across the passband means all spectral components are delayed equally, preserving waveform shape.

Shannon capacity

Channel capacity in bits per second is C = B log2(1 + S/N) for bandwidth B and signal-to-noise ratio S/N. Capacity grows only logarithmically with power but linearly with bandwidth.

Nyquist bandwidth criterion

For zero intersymbol interference, the minimum baseband bandwidth is Rs/2 for symbol rate Rs. Raised-cosine pulses exceed this minimum, trading excess bandwidth for smoother time-domain tails.

FM modulation index

For tone modulation, β = Δf/fm, where Δf is peak frequency deviation and fm is modulating frequency. Carson's rule estimates bandwidth as 2(Δf + fm).

AM modulation index

For amplitude modulation, μ = Am/Ac, the modulating amplitude divided by carrier amplitude. Values above one cause overmodulation and envelope distortion; total power is Pc(1 + μ²/2).

Matched filter

The filter maximizing output signal-to-noise ratio at a sampling instant has impulse response h(t) proportional to s(T − t). Its peak output SNR equals 2E/N0 for energy E.

Hamming distance

The number of bit positions in which two codewords differ. A code with minimum distance dmin corrects up to floor((dmin − 1)/2) errors and detects up to dmin − 1 errors.

Characteristic impedance

For a lossless line, Z0 = √(L/C), where L and C are per-unit-length inductance and capacitance. It relates traveling-wave voltage to current and sets matching conditions.

Reflection coefficient

Γ = (ZL − Z0)/(ZL + Z0) at a load. Its magnitude is at most one for passive loads; VSWR equals (1 + |Γ|)/(1 − |Γ|), equal to one when perfectly matched.

Skin depth

Attenuation in conductors confines current near the surface. Skin depth δ = √(2/(ωμσ)) decreases with increasing frequency, raising effective resistance and conductor loss.

Antenna gain

Gain equals directivity times radiation efficiency. It compares peak radiated intensity to that of an isotropic radiator; effective aperture relates to gain by Ae = Gλ²/(4π).

Friis transmission equation

Received power equals transmitted power times the product of transmit and receive gains times (λ/4πR)². It shows received power falls as the square of distance in free space.

Two's complement range

An n-bit two's complement number spans −2^(n−1) to 2^(n−1) − 1. Negation is bit inversion plus one; overflow is detected when carry into and out of the sign bit differ.

Setup and hold time

Setup time requires data stable before the clock edge; hold time requires it stable after. Violations cause metastability; the clock period must exceed combinational delay plus setup and clock skew.

Karnaugh map grouping

Groups of adjacent ones must be powers of two and as large as possible. Each group yields a product term dropping variables that change; don't-care cells may be included to enlarge groups.