Topic 3: Op-Amp: Golden Rules of OP Amp 1.i in =0, no current flow into op amp. 2.V + =V - Typically one end of op amp is connected to ground, therefore, V + =V - = 0V, virtual ground. Often V + is connected to ground to avoid stability problem. 3.Various circuits: amplifier, sum and abstract, differentiator, integrator, etc.

Example What does the following circuit do? That is, find an expression for the gain and give the circuit a suitable name.

Example II (a) (7pts)The circuit is an integrate circuit. Derive v out (t). R S =10 kΩ, C F =0.008 µF. (b) (5pts)If the input signal v in =sin(2000πt) V, calculate v out (t) and the peak amplitude. (c) (3pts)If the input signal v in =10 mV, calculate v out (t) and v out (t=100ms) (d) (3pts)Op-amp is saturated when the output voltage reach the power supply voltage, ±15V in this case. At what time does the integration of the DC input cause the op-amp to saturated fully? (e) (7pts) If the input signal is now v in =0.01+ sin(2000πt) V, describe what happens to the output waveform till the op-amp is fully saturated.

Example 4 Design an op-amp circuit to convert the triangular waveform v 1 in the following Figure into the square wave v o shown. Use 0.1  F capacitor. (Hints: First quantitatively determine the mathematical expression of v o in terms of v 1 ). v 1 (t)

Topic 4: Filters Low-pass filters (LP)

Active Filter It is phasor time again

Active Low Pass Filter Amplification: R F /R S low pass factor 1/(1+j  R F C F ) Cut off frequency:  R F C F =1 R F /R S =10, 1/R F C F =1

Band-pass Filters and Resonant Circuits Resonant frequency Quality factor

RLC Resonant At resonance: current is max. Z eq =R current and voltage are in phase. the higher Q, the narrower the resonant peak. Applications: tuning circuit

Example a. Write the transfer function for this filter. (Both V in and V out are referenced to ground). b). Design a high-pass RC filter with a characteristic frequency of 80 Hz using a capacitor of 2.0  F. c). What is the new characteristic frequency when the filter is loaded with 50 ohm? How do you solve the problem: Use small R or use active filter

Example 2 The circuit shown in an active filter. Determine: The voltage transfer function. The pass-band gain. RFRF RiRi v+v+

Exam 3 The input signal can be written as V i =10mV(sin10t+sin10,000t). Design a circuit so that the output signal is V 0 =-100mVsin10t. In another words, the high frequency signal has to be much smaller (<1%) than the low frequency part. Low frequency high frequency Check low freq.

Topic 5: Electromachine Motion  Electricity (generator): Magnetic Induction, Faraday’s law Electricity  Motion (motor): force on a current, torque Three phase power: structure, advantages.