Step-by-Step Solution Find the correct value of the current I x . Step 1: Apply the Virtual Ground Concept For an ideal op-amp with negative feedback: The non-inverting terminal (+) is grounded. Therefore, V - = V + = 0 V. No current enters the op-amp input terminals. Step 2: Apply KCL at the Inverting Terminal Let the voltage at the right-hand node be V x . Applying Kirchhoff's Current Law: (2 - 0) / 1k = (0 - V x ) / 1k Therefore, V x = -2 V Step 3: Apply KCL at the Right-Hand Node First, calculate the current through the feedback 1 kΩ resistor: I 1 = [0 - (-2)] / 1k I 1 = 2 mA Next, calculate the curre...

  Q. A complex load (in Ω) is represented as Γ L = 0.5∠30° on the Smith chart. A co-axial cable with a characteristic impedance of 50 Ω is connected to the load. The new input impedance of the load now moves to a diametrically opposite point on the same Γ circle on the Smith chart. Which option is the nearest input impedance of the cable-connected load? Options (A) 20.7 − j5.1 Ω (B) 17.7 − j11.8 Ω ✓ (C) 97.5 − j65.0 Ω (D) 97.5 + j65.0 Ω Step-by-Step Solution Step 1: Given Data Load reflection coefficient: Γ L = 0.5∠30° Characteristic impedance: Z 0 = 50 Ω Step 2: Find the New Reflection Coefficient A diametrically opposite point on the same VSWR circl...

  Q. A small signal source, V i (t) = A cos(10 5 t) + B sin(10 7 t) , is applied to a BJT circuit as shown in the figure. Assume zero source resistance, V BE = 0.7 V, β dc = 99, Early voltage = 100 V and thermal voltage = 25 mV. The effect of internal parasitic capacitances of the BJT may be neglected. Which expression is the best approximation of the output voltage V o (t)? Step-by-step Solution Step 1: Calculate the DC Operating Point Given circuit parameters: V CC = 12 V R 1 = 100 kΩ, R 2 = 25 kΩ R C = 5 kΩ R E = 500 + 1000 = 1500 Ω β = 99, V BE = 0.7 V Thevenin equivalent voltage at the base: V TH = 12 × 25 / (100 + 25) = 2.4 V Thevenin resistance: ...

  Q. A shift-left Shift Register (SR) and a D flip-flop are connected to a synchronized clock as shown in the figure. Assume that the SR and D flip-flops are initially cleared and the XOR gate has no propagation delay. Which of the following options gives the correct binary representation (b 7 b 6 b 5 b 4 b 3 b 2 b 1 b 0 ) of the content of the shift register immediately after the 5 th clock transition (positive edge)? Step-by-step Solution Step 1: Initial Conditions Shift register (SR) = 00000000 D flip-flop output Q = 0 One input of the XOR gate is connected to logic 1. Therefore, the XOR output is: D SR = Q ⊕ 1 = 0 ⊕ 1 = 1 Step 2: Understand the Circuit ...

  Signals and Systems | Fourier Transform Does x(t)e -j2πft Reveal Frequency? Understanding the Fourier Transform The expression x(t)e -j2πft is an important part of the Fourier Transform. It is used to analyse the frequency components present in a continuous-time signal. However, this expression alone does not reveal the complete frequency spectrum. We must integrate it over time to obtain the Fourier Transform X(f). 1. What Is the Fourier Transform? The Fourier Transform is a mathematical operation that converts a signal from the time domain into the frequency domain. It helps us understand which frequencies are present in a signal and their corresponding magnitude and phase. Continuous-Time Fourier Transform Formula X(f) = ∫ −∞ ∞ x(t)e −j2πft dt Meaning of E...