Applications of operational Amplifiers UNIT 3 Applications of operational Amplifiers

Oscillators Oscillators are circuits that generate periodic signals An oscillator converts DC power from the power supply into AC signal power spontaneously - without the need for an AC input source Figure 9.67 Repetitive ramp waveform.

Linear Oscillators Figure 9.68 A linear oscillator is formed by connecting an amplifier and a feedback network in a loop.

Barkhausen Criterion Figure 9.69 Linear oscillator with external signal Xin injected.

Barkhausen Criterion

How does the oscillation get started? Noise signals and the transients associated with the circuit turning on provide the initial source signal that initiate the oscillation

Practical Design Considerations Usually, oscillators are designed so that the loop gain magnitude is slightly higher than unity at the desired frequency of oscillation This is done because if we designed for unity loop gain magnitude a slight reduction in gain would result in oscillations that die to zero The drawback is that the oscillation will be will be slightly distorted (the higher gain results in oscillation that grows up to the point that will be clipped)

Example of Oscillator circuit (1) Figure 9.70 Typical linear oscillator.

Example of Oscillator circuit (2) Figure 9.71 Feedback network. Note that the input to the network is on the right-hand side and the response is on the left-hand side.

Wien-Bridge Oscillator Figure 9.73 Wien-bridge oscillator.

Wien-Bridge oscillator output Figure 9.75 Example of output voltage of the oscillator.

Methods for Amplitude Stabilization In a linear oscillator, amplitude stabilization below the amplifier clipping level is needed to reduce distortion We can reduce the amount of distortion by reducing the amplifier gain However, if the gain becomes too small the oscillations die out Several approaches can be used to resolve the conflict The easiest approach is to make the gain adjustable by using a potentiometer in place of the resistors that determine the gain

Inverting Amplifier R vo Rf R v R www.Vidyarthiplus.com Inverting Amplifier o 10 V i Rf i Ri  -10 V 10 V i o i + Slope = -R / Ri f (a) -10 V R vo Rf (b) f i R v R i i i (a) An inverting amplified. Current flowing through the input resistor R also flows through the i feedback resistor R . f (b) The input-output plot shows a slope of -R / R in f i the central portion, but the output saturates at about ±13 V.

Non-inverting Amplifier Ri Rf Slope = (R + R )/ R f i i -10 V 10 V i - o -10 V i + R  Ri R  R  R  f f i f vo  vi G   1    Ri Ri R   i

Summing Amplifier

Summing Amplifier  v v  v  R     R R   Rf R1 1 R2 o 2 1 2 +  v v  v  R  1  2   o f R R   1 2

Summing Amplifier

Non Inverting Summer

Adder-Subtractor

Op-amp Differentiator Applying KCL at inverting node of opamp, we get (0-V )/R + I = 0 out c I = V /R c out where I = C*d(0-V )/dt. Hence we get V = -R*C*dV /dt. c in out in

Op-amp Differentiator

Improved Op-amp Differentiator

Opamp Integrator Applying KCL at inverting node of opamp, we get (0-V )/R + I = 0 out c Ic = Vout/R= 1/C

Practical Integrator

Differential Amplifier

Differential Amplifiers Differential Gain Gd  v3 vo R4 G   d v  v R 3 v4 4 3 Common Mode Gain Gc  ◦ For ideal op amp if the inputs are equal then the output = 0, and the G = 0. c R 4 ◦ No differential amplifier perfectly rejects v  (v  v ) o 4 3 the common-mode voltage. R 3 Common-mode rejection ratio CMMR  ◦ Typical values range from 100 to 10,000 CMRR Gd Gc Disadvantage of one-op-amp differential amplifier is its low input resistance

An instrumentation amplifier is used to measure and control physical quantities such as temperature, humidity, light intensity, and waterflow.

signal from the transducer  Instrumentation amplifier is the front end component of every measuring instrument which improves the signal to noise ratio of the input electrical signal from the transducer

Instrumentation Amplifiers Differential Mode Gain v  v  i(R  R  R ) 3 4 2 1 2 v  v  iR 1 2 1 v  v 2R  R 1 G  3 4  2 Advavntagves: HigRh input impedance, High CMRR, d 1 2 1 Variable gain

Instumentation Amplifier

Follower ( buffer) resistance from being loaded down by a  Used as a buffer, to prevent a high source resistance from being loaded down by a low-resistance load. In another word it prevents drawing current from the source.  o i + vo  vi G 1

Current to Voltage Converter (Transresistance Amplifier)

Voltage to Current Converter (Transconductance Amplifier)

Voltage to Current Converter (Transconductance Amplifier)

Transconductance amplifier with floating Load

Filter passes signal of specified Band of frequencies and the band  Filter is a frequency selective circuit that passes signal of specified Band of frequencies and  attenuates the signals of frequencies outside the band  Type of Filter  1. Passive filters  2. Active filters

low Q,resulting in high power dissipation  Passive filters  Passive filters works well for high frequencies. But at audio frequencies, the inductors become problematic, as they become large, heavy and expensive.  For low frequency applications, more number of turns of wire must be used which in turn adds to the series resistance degrading inductor’s performance ie, low Q,resulting in high power dissipation  Active filters  Active filters used op- amp as the active element and resistors and capacitors as passive elements.  By enclosing a capacitor in the feed back loop , inductor less active filters can be obtained

• Active filters use op-amp(s) and RC components. • Advantages over passive filters: – op-amp(s) provide gain and overcome circuit losses – increase input impedance to minimize circuit loading – higher output power – sharp cutoff characteristics some commonly used active filters 1. Low pass filter 2. High pass filter 3. Band pass filter 4. Band reject filter Active Filters can be produced simply and efficiently without bulky inductors

Review of Filter Types & Responses • 4 major types of filters: low-pass, high-pass, band pass, and band-reject or band-stop • 0 dB attenuation in the pass band (usually) • 3 dB attenuation at the critical or cutoff frequency, fc (for Butterworth filter) • Roll-off at 20 dB/dec (or 6 dB/oct) per pole outside the passband (# of poles = # of reactive elements). Attenuation at any frequency, f, is • Bandwidth of a filter: BW = fcu - fcl • Phase shift: 45 /pole at fc; 90o/pole at >> fc o • 4 types of filter responses are commonly used:

Types of filters •Butterworth - maximally flat in passband; highly non-linear phase response with frequency •– Bessel - gentle roll-off; linear phase shift with freq. •– Chebyshev - steep initial roll-off with ripples in passband •– Cauer (or elliptic) - steepest roll-off of the four types but has ripples in the passband and in the stop band

Frequency response of filters

I order Active LPF

I order Active HPF

Wide BPF