It is the ratio of differential voltage gain Ad to the common mode voltage gain Acm. | unit 1 operational amplifier fundamentals

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UNIT-1Operational AmplifierQ1) Design a non-inverting amplifier using Op-amp with a closed loop voltage gain of 10. A1) Af = 1 + Rf/R1 =10 Rf/R1 = 9Rf = 9 R1 If R1 = 1KRf = 9K Ω

Substitute values in above figure. This is the required non-inverting amplifier circuit Q2) In an op-amp inverting amplifier R1 = 1K Ω and Rf = 100KΩ. The DC supply voltage of the op-amp is ± 15V. Calculate the output voltage if input voltage is 1V. A2)

R1 = 1KΩ Rf = 100KΩ

V+ = 15V and V-=-15V. vi = 1V

Af = -Rf/R1 = -100K/1K = -100

Af = vo/vi

Vo = Af vi

= -100 x 1V = -100V

The output voltage cannot exceed the DC power supply voltage. Since vo is negative and large it is limited to V-

Vo ≈ V- = -15V

Q3) A 200mV peak to peak sine waveform voltage is applied to Op-amp inverting amplifier with Rf/R1 = 10. A3)

Peak to peak input voltage

2Vm = 200 mV

Vm = 100 mV

Vi= Vm sin wt = 100 sin wt mV

Vo = -Rf/R1 x vi = -10 x 100 sinwt mV

= -1000 sin wt mV

Q4) In a summing amplifier, if R = 1kΩ, Va = +3V, Vb = +8V, Vc = +9V, Vd = +5V and supply voltage is ±15V. Find the output voltage Vo.A4)

Vo = Sum of all input voltages applied at both the terminals

Vo = Va + Vb + Vc +Vd

Vo = -3 -8 +9 +5

Vo = +3V

Q5) Find the output voltage for the given circuit diagram if Rf = 5kΩ.

A5) We know,

Gain (Av) = =

Hence,

Av1 =

Av2 =

Now, Output voltage Vo = Sum of the two amplified input signals

Vo = Av1 x V1 + Av2 x V2

Vo =(-5 x 3) + ( -2.5x 4) mV

Vo = -25mV

As the above output voltage is negative hence it is an inverting amplifier.

Q6) Draw and explain the difference amplifier?A6)

Fig 1: Difference amplifier

Here input can be provided simultaneously at both the terminals of amplifier.

Voltage signal Va is applied at one input terminal and another voltage signal Vb onto the other input terminal then resultant output voltage is proportional to the “Difference” between the input voltages Va and Vb.

Vo = Vb - Va

Now by applying superposition theorem we get,

Summing point, V1 = V2 and

V2 = Vb

If Vb = 0 then

And Va = 0 then

Vo = -V01 + V02

Vo = +

If R1 = R2 and Rf = R4 then

And if R1 = R2 = Rf = R4 =R then

Vo = Vb – Va

Hence, is known as a Unity Gain Differential Amplifier. Q7) Derive the expression of op-amp output for non-inverting summing amplifier?A7)

Fig 2: Non-Inverting Summing Amplifier

Applying KCL to the above circuit we have

IR1+IR2 = 0

= = 0

When R1 = R2 =R

V+ =

The voltage gain for non-inverting summing amplifier is given as

AV = Vout/Vin = = 1+

Vout= [1+]

Q8) Derive the expression of closed loop voltage gain for inverting amplifier?A8)

Fig 3 Non-Inverting AmplifierThe input signal vi is applied to the inverting input terminal through resistor R1 and non-inverting input terminal is grounded. The feedback from the output of the inverting terminal is provided through the feedback resistor Rf. Since the input is applied to the inverting terminal vo and vi are opposite in polarity and hence the feedback is negative. Since the non-inverting input terminal is grounded v2=0. Due to virtual short at the input of op-amp the inverting and non-inverting input terminals are at the same potential. Therefore, v1 = v2 = 0.

Due to high input impedance of Op-amp the current flowing into its inverting input terminal is zero. Therefore, the same current flows through R1 and Rf .

i 1 = i f

But i1 = vi – v1 / R1 = vi/R1

i f = v1 – vo / Rf = -vo/Rf

vi/R1 = - vo/Rf

Af = vo/vi = -Rf/R1

Af is the closed loop voltage gain or voltage gain with negative feedback. Q9) What are voltage follower explain and derive the output equation?A9) It is called as voltage follower because output voltage follows input voltage. It is basically a non-inverting amplifier with amplifier gain is unity. The gain of non-inverting amplifier is given byAv = 1+Rf/R1

Fig 4 Voltage FollowerIn voltage follower feedback resistor is zero because output is directly shorted to input therefore Rf=0Av = 1Av = Vo/ViVo=Vi Q10) Define CMRR and SVRR of op-amp?A10)

It is the ratio of differential voltage gain Ad to the common mode voltage gain Acm. CMRR =