# Category: Uncategorized #### 2. Apply the Fourier transform properties to compute the Fourier transform X j ( ω) of the signal x t( )that is shown in the following figure. Please list the detail steps to receive full credit [25 points].

... #### 1. The following are impulse response of discrete-time and continuous-time LTI systems. Determine whether each system is causal and/or stable. Justify your answers [20 points].

... #### 1. Assume *** Answer format: Q points (voltage , current) – example (1.03 , 0.87) ; Do not include units . Round your answer to two decimal places ***

... #### 6. [20 pts] Design a circuit using a pnp transistor for which � ≅ 1 using two resistors connected appropriately to ±3 � so that IE = 0.5 mA and VBC = 1 V. (a) Draw your design circuit with the appropriate electronic components and connections. (b) What exact values of RE and RC would be needed?

... #### 5. [20 pts] A pnp transistor model with the circuit shown below is connected with its base at ground, collector at -2.0 V, and a 1 mA current is injected into its emitter. Assume the transistor is operating in the active mode region. (a) If the transistor is said to have β=10, what are its base and collector currents? (b) In which direction do they flow? (c) If Is = 10-15 A, what voltage results at the emitter? (d) What does the collector current become if a transistor with β=1000 is substituted?

... #### 4. [15 pts] The NMOS transistors in the circuit shown below have Find the required values of gate width for each Q1, Q2, and Q3 to obtain the voltage and current values indicated.

... #### 3. [20 pts] Consider the half-wave rectifier shown below with the diode reversed. Let vs be a sinusoid with 10-V peak amplitude, and let R = 1 kΩ. Use the constant-voltage-drop diode model with VD = 0.7 V. (a) Sketch the transfer function (b) Sketch the waveform of v0. (c) Find the average value of v0. (d) Find the peak current in the diode. (e) Find the PIV of the diode.

... #### 2. [10 pts] In a 10-µm-long bar of donor-doped silicon, what donor concentration is needed to realize a current density of 2 mA/µm2 in response to an applied voltage of 1 V? (Hint: Although the carrier mobilities change with doping concentration, as a first approximation you may assume µn to be constant and use 1350 , the value for intrinsic silicon.)

... #### 1. [15 pts] The inverting circuit with the T network in the feedback is shown below in a way that emphasizes the observation that R2 and R3 in effect are in parallel (because the ideal op-amp forces a virtual ground at the inverting input terminal). Use this observation to derive an expression for the gain by first finding and . For the latter use the voltage divider method applied to R4 and (R2llR3).

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