(a) For the Schottky transistor circuit shown below, determine I_B, I_D, I_C and V_CE. Next, remove the Schottky diode and determine I_B, I_D, I_C and V_CE assuming additional values of V_BE (sat.) = 0.8 V and V_CE (sat.) = 0.1 V. Assume parameter va

Question

(a) For the Schottky transistor circuit shown below, determine I_B, I_D, I_C and V_CE. Next, remove the Schottky diode and determine I_B, I_D, I_C and V_CE assuming additional values of V_BE (sat.) = 0.8 V and V_CE (sat.) = 0.1 V. Assume parameter values of β = 50, V_BE (on) = 0.7 V and V_f = 0.3 V for the Schottky diode. (20 marks)

(b) Find the Fourier transform of the following signals:
(i) x(t) = [2sin(3πt)/πt] · [sin(2πt)/πt]
(ii) x(t) = ∫_{-∞}^{t} [sin(2πt)/πt] dt
Specify the properties used. (20 marks)

(c) In the circuit shown below, V_s is the ac voltage source given by V_s = V_0 cos ωt, with V_0 = 14.14 V and ω = 300 rad/sec. Calculate the value of load resistance R_L for maximum power transfer and also find out maximum power transferred to load. k = 1, n = 0.2 (Turns Ratio) (10 marks)

UPSC Answer Check · Accepted Answer

Solve this multi-part numerical problem by allocating approximately 40% of effort to part (a) Schottky transistor analysis (20 marks), 40% to part (b) Fourier transform computations (20 marks), and 20% to part (c) maximum power transfer (10 marks). Begin with clear circuit diagrams for parts (a) and (c), then proceed with systematic calculations showing all intermediate steps. For part (b), explicitly state each Fourier property used before applying it. Conclude each sub-part with boxed final answers and brief physical interpretations.
- Part (a): Correct determination of I_B, I_D, I_C, V_CE with Schottky diode clamping (V_f = 0.3V), then recalculation without Schottky showing deep saturation (V_BE(sat)=0.8V, V_CE(sat)=0.1V)
- Part (b)(i): Application of multiplication-convolution duality property to find FT of product of two sinc functions, yielding triangular convolution of rectangular pulses in frequency domain
- Part (b)(ii): Use of time-integration property of FT (division by jω in frequency domain plus πδ(ω) term) applied to sinc function, recognizing integral of sinc as step response
- Part (c): Calculation of reflected impedance through coupled inductors (k=1, n=0.2), determination of Thevenin equivalent seen by load, and application of conjugate matching for maximum power transfer at ω=300 rad/s
- Explicit statement of Fourier properties used: multiplication-convolution duality for (b)(i), time-integration property for (b)(ii)

Dimension	Weight	Max marks	Excellent	Average	Poor
Concept correctness	25%	12.5	Correctly identifies Schottky transistor's clamping action preventing deep saturation; accurately applies Fourier transform properties (convolution theorem, integration property); properly models coupled inductor circuit with perfect coupling (k=1) and turns ratio effects	Minor errors in applying one Fourier property or misunderstanding Schottky diode's role in limiting V_BC; correct basic approach but some conceptual gaps in coupled inductor modeling	Fundamental misconceptions such as treating Schottky diode as regular diode, confusing time multiplication with frequency multiplication, or ignoring coupling coefficient in inductor calculations
Numerical accuracy	25%	12.5	All numerical values accurate to appropriate significant figures: correct currents in mA range for transistor, proper Fourier coefficients, exact maximum power transfer condition with P_max in watts correctly calculated from V_0=14.14V (RMS=10V)	Correct methodology but arithmetic errors in 1-2 sub-parts; acceptable final answers with minor calculation slips; correct order of magnitude but imprecise values	Major calculation errors, wrong orders of magnitude, or incorrect unit conversions; failure to distinguish peak vs RMS values in power calculation
Diagram quality	15%	7.5	Clear hand-drawn circuit diagrams showing Schottky diode placement in (a), proper coupled inductor dot convention in (c); labeled component values; optional frequency domain sketches for (b) showing rectangular pulse spectra	Basic circuit diagrams present but lacking clarity in component labeling or missing dot convention for coupled inductors; adequate but not exemplary	Missing essential diagrams, incorrect circuit topology, or illegible sketches; failure to show Thevenin equivalent for part (c)
Step-by-step derivation	25%	12.5	Systematic KVL/KCL application for transistor bias points; explicit convolution integral setup for (b)(i); clear impedance reflection calculation (Z_L' = Z_L/n²) for coupled inductors; each mathematical step justified	Correct overall approach but skips some intermediate steps; jumps from setup to solution without showing key algebraic manipulations; adequate but condensed derivations	Missing derivation steps, unexplained jumps in logic, or purely final answers without working; failure to show Thevenin equivalent derivation for maximum power transfer
Practical interpretation	10%	5	Briefly explains Schottky clamping's advantage in high-speed switching (reduced storage time); comments on physical meaning of Fourier results (bandwidth, signal energy); notes practical significance of maximum power transfer in transformer-coupled systems	Minimal physical interpretation; standard concluding statements without specific insight into circuit behavior or signal characteristics	Purely mathematical treatment with no physical interpretation; failure to recognize why Schottky transistor is used or what maximum power transfer implies practically

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