Assignment 1

1. The filament of a small vacuum tube uses a power of approximately 1.5 W. Suppose that 75 million of these tubes are used to build the equivalent of a 64-Mb memory. How much power is required for this memory? If the power is supplied from a 230V ac source, what is the current required by this memory?

2. Determine the resistance of a cube with sides of length ‘l cms’ and resistivity ‘10Ω-cm’, when a pair of opposite surfaces are chosen as the terminals.

3. An 8-bit A/D converter has VFS=5V. What is the value of the LSB? If the input voltage is 2.77V, What is the binary output code of the converter?

4. An given signal source provides an open-circuit voltage voc,and a short-circuit current isc. For the following sources, calculate the internal resistance, Rs, the Norton current, is; and the thevenin voltage, vs:(a) voc=10V , isc=100μA(b) voc=0.1V , isc=10μA

5. What is the fundamental frequency of the highest frequency square wave for which the fifth harmonic is barely audible by a relatively young listener?

6. An amplifier using balanced power supplies is known to saturate for signals extending within 1.5 V of either supply. For liner operation, its gain is 500V/V. what is the rms value of the largest un-distorted sine wave output available, and input needed with ±5-V supplies? With ±12-V supplies?

7. An amplifier has a voltage gain of 32 for frequencies above 10 kHz, and zero gain for frequencies below 10 kHz. Classify the amplifier. An input signal given by vs ( t )= (0.5sin 2500 πt+0.75cos 8000πt+0.6 cos12000πt )V is applied to the amplifier. Write the expression for the output voltage of the amplifier.

8. A certain box known to contain only linear elements (and no independent sources), is connected as shown in Figure 1(a). The current waveform i(t) has the form shown in Fig 1(b). The voltage v is zero for all t<0, and is 1 volt for 0<t<2. What is v during the interval from t=2 to t=5? Show one simple possibility for the circuit in the box.

Fig 1(a) Fig 1(b)

9. As illustrated in Fig 2, a capacitor and resistor can be used to filter or smooth the waveforms say from a half-wave rectifier, to get something close to a dc voltage at the output, for use in a power supply, for example.

Fig 2

For simplicity, assume the voltage from source vs is a square wave. Assume that at t=0, vo=0that is the circuit is at rest. Now assuming that R is small enough to make the circuit time constant much smaller than t 1 or t 2, calculate the voltage waveforms for each half cycle of the input wave. Find the average value of the output voltage vofor t 1=t 2. Sketch the waveform clearly.

10.A high performance microprocessor design requires 10 million logic gates and is placed in a package that can dissipate 40W. (a) What is the average power that can be dissipated by each logic gate on the chip? (b) If a supply voltage of 3.3V is used, how much current can be used b each gate? (c) What is the total current required b the microprocessor?