Analog Electronics Test 2

• An operational amplifier is a DC-coupled high gain electronic voltage amplifier with a differential input and usually a single-ended output.
• The input offset voltage is defined as the voltage that must be applied between the two terminals of the op-amp to obtain zero volts at the output.
• Ideally, the difference between both input offset voltages should be zero for zero output voltage. Differential offset voltage = 0 for V_out = 0
• Slew rate is defined as the maximum rate of change of an op amp’s output voltage and is given units of volts per microsecond.
• Ideally for infinite bandwidth of op-amp phase shift is zero and the slew rate is also infinite.
• The phase shift of op-amp is defined as how far the function is shifted (horizontally or vertically from the usual position).

• Negative feedback reduces the gain of the system by a factor of (1 + Aβ). Thus, because of feedback configuration, voltage gain will be decreased by a factor (1 + Aβ).
• Voltage series type feedback tells us that the input of the system is series connected with the feedback loop and series connection corresponds to increased impedance. Therefore the input impedance will be increased by a factor (1 + Aβ).

Chebyshev Filter:

• It is also called an equal rip­ple filter.
• It gives a sharper cut-off than Butterworth filter in the passband.
• It has a ripple response in the passband and flat response in the stopband. it is also known as an equal-ripple response.
• Both Butterworth and Chebyshev filters exhibit large phase shifts near the cut-off frequency.
• A drawback of the Chebyshev fil­ter is the appearance of gain maxima and minima below the cut-off frequency.
• This gain ripple, ex­pressed in dB, is an adjustable parameter in filter design.
• A Chebyshev filter is used where a very sharp roll-off is required. However, this is achieved at the expense of a gain ripple in the lower frequency passband.

Butterworth Filter:

• This filter is also called a maximally flat or flat filter. This class of filters approximates the ideal fit in the passband. 
• it's filter response characterized by flat passband. it is also known as a maximally flat response.
• The Butterworth filter has an essentially flat amplitude-fre­quency response up to the cut­off frequency. 
• Butterworth filters have the sharpest attenuation, their phase-shift as a function of frequency is non-linear.
• It has a monotonic drop in gain with frequency in the cut-off region and a maximally flat response below the cut-off frequency.
• The Butterworth filter has characteristics somewhere be­tween those of Chebyshev and Bessel filters.
• It has a moderate roll-off of the skirt and a slightly non­linear phase responses.