EMWTL - ELECTROSTATICS - PART-1

Electromagnetic Waves and Transmission Lines (EMWTL)

S S Kiran describes about Electrostatics Part-1 

https://youtu.be/d1TrHOhXEdI

Video Link :
https://youtu.be/d1TrHOhXEdI

Channel Link:

https://www.youtube.com/channel/UCtzuJLOveI88Oq3hwj7iRyg

Operational Amplifier Notes Unit -2

Operational Amplifier 

• Characteristics of OP-Amps
• Integrated circuits-Types
• Classification, Package Types and Temperature ranges
• Power supplies, Op-amp Block Diagram
• Ideal and Practical Op-Amp Specifications
• DC and AC characteristics
• 741 op-amp & its features
• Op-Amp parameters & Measurement
• Input & Out put Off set voltages & currents, slew rate
• CMRR, PSRR, drift, Frequency Compensation techniques

Non- Inverting Mode Amplifier

Non- Inverting Amplifier

A voltage follower (also called a unity-gain amplifier, a buffer amplifier, and an isolation amplifier) is an op-amp circuit which has a voltage gain of one. Voltage followers are generally used to isolate stages from each other. A voltage follower generally has high input impedance and low output impedance.

If the signal is applied to the non-inverting input terminal and feedback is given as following figure, the circuit amplifies without inverting the input signal. Such a circuit is called non-inverting amplifier. It may be noted that it is also a negative feed-back system as output is being fed back to the inverting input terminal.

As the differential voltage v_d at the input terminal of op-amp is zero, the voltage node a in above figure is v_i , same as the input voltage applied to non-inverting terminal. Now R_f and  R₁ forms a potential divider. Hence

as no current flows into the op-amp

A non-inverting amplifier is an op-amp circuit configuration which produces an amplified output signal. This output signal of non-inverting op amp is in-phase with the input signal applied. In other words a non-inverting amplifier behaves like a voltage follower circuit.

A voltage follower (also called a unity-gain amplifier, a buffer amplifier, and an isolation amplifier) is an op-amp circuit which has a voltage gain of one. Voltage followers are generally used to isolate stages from each other. A voltage follower generally has high input impedance and low output impedance.

The basic non-inverting amplifier circuit using an op-amp is shown above. In this circuit the signal is applied to the non-inverting input of the amplifier. However the feedback is taken from the output via a resistor to the inverting input of the operational amplifier where another resistor is taken to ground. It is the value of these two resistors that govern the gain of the operational amplifier circuit.

The gain of the non-inverting amplifier circuit for the operational amplifier is easy to determine. The calculation hinges around the fact that the voltage at both inputs is the same. This arises from the fact that the gain of the amplifier is exceedingly high. If the output of the circuit remains within the supply rails of the amplifier, then the output voltage divided by the gain means that there is virtually no difference between the two inputs.

As the input to the op-amp draws no current this means that the current flowing in the resistors R1 and R2 is the same. The voltage at the inverting input is formed from a potential divider consisting of R1 and R2, and as the voltage at both inputs is the same, the voltage at the inverting input must be the same as that at the non-inverting input. This means that V_in = V_out x R1 / (R1 + R2). Hence the voltage gain of the circuit Av can be taken as

Applications:

Op amp as a voltage follower

A non-inverting amplifier using an op amp forms an ideal voltage follower. The very high gain of the op amp enables it to present a very high impedance to the signal source whilst being able to accurately follow the voltage waveform.

An op amp is configured in its non-inverting amplifier format, linking the output directly to the inverting input and applying the input signal to the non-inverting input.

From the gain equation it is possible to see that the voltage gain of this circuit is unity.

Av = 1 + R2 / R1.

R2 is zero and R1 is infinity,

So the term R2/R1 is zero and this means that A_v = 1 (Unity Gain)

Inverting Mode Amplifier

Inverting Operational Amplifier

The most widely used of all the op-amp circuits, the circuit is shown in figure. The output voltage V₀ is fed back to the inverting input terminal through the R_f - R₁ Network where R_f is the feedback resistor. Input signal V_i is applied to the inverting input terminal through R₁ and non- inverting input terminal of op-amp is grounded.

Consider as V_d = 0, node a is at ground potential and the current i₁ through R₁ is

also since op-amp draws no current, all the current flowing through R₁  must flow through R_f. The output voltage

Hence, the gain o f the inverting amplifier (also referred as closed loop(CL) gain) is,

Alternatively, the nodal equation at the node ‘a’ in following figure is

Where v_a  is the voltage at node ‘a’. Since node ‘a’ is at virtual ground v_a = 0, Therefore, we get

Physical diagrammatical phenomena of Inverting Amplifier: The basic circuit for the inverting op amp circuit is shown below. It consists of a resistor from the input terminal to the inverting amplifier input of the circuit, and another resistor connected from the output to the inverting input of the op-amp. The non-inverting input is connected to ground.

The negative sign indicates a phase shift of 180 degrees between v_i and v₀ .  In this inverting amplifier circuit the non-inverting input of the operational amplifier is connected to ground. As the gain of the op amp itself is very high and the output from the amplifier is a matter of only a few volts, this means that the difference between the two input terminals is exceedingly small and can be ignored. As the non-inverting input of the operational amplifier is held at ground potential this means that the inverting input must be virtually at earth potential. As a result, this form of amplifier is often known as a virtual earth amplifier.

Input impedance:   With the value of R₁, the input resistor being lower than the feedback resistor R_f, care has to be taken when designing he circuit to ensure the input resistance is not too low for any given application. Often values of 10kΩ are used as this provides a reasonable load resistance for many circuits. However the exact requirements need to be determined for each application.

Range of values for R1 and R2:   R_f must be higher. Even though the input impedance of the integrated circuit itself circuit may be high, using a high value of feedback resistor is not advisable as results may become a little unpredictable. As a very broad rule of thumb values for R_f of up to 100kΩ or a little more should be fine.

Summing amplifier or virtual earth mixer

The fact that the inverting input to the amplifier is virtually at earth potential provides some significant possibilities for audio mixer applications.

This form of virtual earth mixer or summing amplifier adds several different signals in a linear or additive fashion. It is not the form of multiplier mixer used in RF circuits where a non-linear action is used.