4. Simplify the following functions using a bound: \text { A. }\left(2^{n}+90\right)\left(2^{n}+10\right)+n^{1000} \text { B. } \sum_{i=0}^{n} i^{2} n^{i} \text { C. } 100 x^{10}+90 x^{9}+80 x^{8}+70 x^{7}+60 x^{6}+50 x^{5}+40 x^{4}+30 x^{3}+20 x^{2}+10 x

1. Let us plot the Shockley diode equation. Suppose you are required to use In () as the vertical axis and V as the horizontal axis. Plot the result qualitatively and correctly label relevant parameters, i.e. axis intercepts and polynomial coefficients. Between a forward bias of 0.65 V and 0.75 V, how much does In / increase?

(5 pts.) Given an analog output signal whose voltage should range from 0 to 10V, and an 8-bitdigital encoding, provide the encodings for the following desired voltages: (a) OV, (b) 1V, (c) 5.33V,(d) 10V, what is the resolution of the conversion?

The Voltage across the Capacitor is given by the formula: V_{c}=V_{i n}\left(1-e^{-\frac{t}{R C}}\right) Using the formula, calculate the time taken for the capacitor to charge to 1/2Vin Given that C=120NF R=47kOhms. Give your answer in milli-Seconds.

11) The cut-off frequency for an RC Low pass filter circuit is the frequency atwhich: R=\frac{1}{2 \pi f C} Calculate the cut-off frequency using the following values for R and C: R=4.7kOhmsC=0.22MicroFarads. Give your answer in Hz

Fig Q3(al) is a load line diagram of the diode and resistor circuit shown schematically in Fig Q3(a2). What is the value of RL and the maximum value of Vs of the circuit?[- Fig Q3(b) is a full wave rectification circuit. Sketch the input and output voltage waveforms (Vin and Vout) using the fact that Cs=1 µF, RL = 10KOhm, 1KHZ – AC signal and 10V peak to peak value of theVin-[7] Now replace the smoothing capacitor Cs with a value 0.01 µF and on the same figure that you made above (where you have Cs=1 µF) add a second output waveform to the sketch for this situation.[3] Explain why the output waveform has been modified as a result of changing the value of the smoothing capacitor.[2] Sketch a schematic view of a possible circuit design for single stage amplifier circuit based on a single stage field effect transistor with the following characteristics: i) Voltage gain ~ 1 ii) Large input impedance iii) Small output impedance

A Keyboard instrument having an output impedance of 200 Ohms is mistakenly plugged into the Low impedance microphone input socket on an amplifier. If the microphone input has an input impedance of 3002. Calculate the resulting signal loss Vo/Vin.

Which of the following statements about transistor operation are true? 1The main current flow is from the base to the emitter The main current flow is from the Collector to the Emitter 3The current flowing in the base is greater than the current flowing in the collector 4The current flowing in the base controls the current flowing in the collector 5The current flowing in the emitter is the sum of the base current and collector current 6The current flowing in the emitter is the collector current minus the base current

Given is an OpAmp which is connect to a square-wave generator. The output voltage of the OpAmp follows a first-order response, and the rise-time is measured to be 1us. Determine the cut-off frequency, give you answer in Hz, and write your answer without the unit.

Below is a passive filter circuit shown in figure Q2. For the following parts, include all calculations and equations used. Component values are: R1 = 1 KQ, R2 = 3300, R3=1.8 KQ, R4 = 2700, R5= 6600, C1= 10nF, C2 = 0.01μF, C3 = 20nF. a) Identify what the cut off frequency of the circuit is. (10 marks) b) What is the roll-off or slope for this circuit in the stop band and why? (6 marks) c) Vin If R5 was not correctly placed in the breadboard and fell out of the breadboard completely, would the cut off frequency increase or decrease, justify your decision? (4 marks) C1 H C3 C2 HH R1 R2 R3 R4 GND Figure Q2. Passive filter circuit R5 V out

Question 5: Figure 5 shows a feedback trans-conductance amplifier implemented using an op amp with open-loop gain µ, a very large input resistance, and an output resistance r.. The output current I that is delivered to the load resistance RL is sensed by the feedback network composed of the three resistances RM, R¹, and R2, and a proportional voltage Vf is fed back to the negative input terminal of the op amp. a) Find the expression for A, = 1/V₂. b) If the loop gain is large, find an approximate expression for A, and state the condition for which this applies.