# Electronic Circuits

## Operational Amplifiers

An *Operation Amplifier* is a device which, when powered by *non-inverting* (*inverting* (

Where no input current enters *input impedance is infinite*.

Ideal Op Amp

**Open Loop Gain**, where the output and inputs have not been connected. The **Closed Loop Gain** will be denoted as

The **Differential Input Signal** **Common Mode Input Signal**

### Inverting Configuration

In the inverting configuration, the output of the op-amp is connected back into the inverting terminal. Because in the inverting configuration *closes the loop* around the op amp so that it provides a stable output.

In the case where a resistance is placed between **Positive Feedback**, and the output would increase exponentially.

Inverting Configuration of Op Amp

If

This is known as a *Virtual Short Circuit*.

The **Closed Loop Gain**

From Figure 1, we can see that knowing

Closed Loop Gain of a Non-Inverting Amplifier

#### Finite Open-Loop Gain

When the open-loop gain

#### Input and Output Resistance

The input resistance is equal to

#### Weighted Summer

In this configuration,

In the case where a design must be created to fit an equation with multiple inverted signs, two op-amps can used in series to flip the initial signals.

Weighted Summers in Series

### Non-Inverting Configuration

The Non-inverting configuration occurs when a voltage input enters the

The

Closed Loop Gain of a Non-Inverting Amplifier

#### Finite Open-Loop Gain

When the open-loop gain

#### Buffering Amplifier or Voltage Follower

In this configuration, the loop is closed by short circuiting the output to non-inverting input. This will again create a virtual short circuit between

Buffer Amplifier or Voltage Follower

### Difference Amplifiers

A Difference Amplifier is one where voltage sources are applied to the

In a case like this, *common-mode rejection ratio (CMRR)*

Common Mode Rejection Ratio

In a Difference amplifier with voltage sources at

Therefore,

To find values concering solely the

Difference Amplifier

#### Instrumentation Bridge Amplifiers

The Instrumentation Bridge Amplifier is a Difference Amplifier created as a solution to the low input resistance of Difference Amplifiers, without sacrificing ease of control. From Figure 6, it can be noted that

Output of the Instrumentation Bridge Amplifier

## Filters and Tuned Amplifiers

A filter is a linear two-port network with a transfer function

Note on Imaginary Numbers:

Magnitude =

Phase =

### Filter Transmission

The transmission characteristics of a filter are specified in terms of the edges of the passband(s)

General First-Order Transfer Function

The filter transfer function can be expressed as the ratio of two polynomials in

### Filter Types

**High Pass** allows high frequencies to pass through (the *passband*) and attenuates frequences below (the *stopband*).

**Low Pass** allows low frequencies to pass through.

**Band Pass** will pass all bands, but invert phase.

**Band Stop** will stop all bands within the specified range.

In each case of attenuation, the slope will be -20 dB per decade.

The **All Pass Filter** is a special case which does not attenuate, but serves as a phase shifter, with a unity gain and phase shift at

### Filter Transmission (2nd Order Filters)

General Second-Order Transfer Function

### Filter Types

**High Pass** goes zero as the

**Low Pass** allows low frequencies to pass through.

**Band Pass** will attenuate all but the

**Notch** will attenutate at the center frequency

$Q = 1/\sqrt{2} = $The Butterworth Maximally Flat Response

### Second Order LCR Resonator

Resonators are used to realize second order filters.

For a current applied to this circuit,

In this case,

Using this structure,

By following the structure

#### Antoniou Inductance Circuit

Inductors in the resonator circuits can be replaced by a system of op amps, such as the *Antoniou Inductance Simulation Circuit*.

From the circuit below, an impedance

The design of this circuit is usually based on selecting

This circuit would have a pole frequency

The gain would be derived from

#### Filter Types

The position of the capacitor

### Second Order Active Filters Based on Two Integrators

Biquads based on the two-integrator-loop topology are the most versatile and popular second-order filter realizations. There are two varieties: the KHN circuit, which realizes the LP, BP, and HP functions simultaneously and can be combined with the output summing amplifier to realize the notch and all-pass functions; and the Tow–Thomas circuit, which realizes the BP and LP functions simultaneously. Feedforward can be applied to the Tow–Thomas circuit to obtain the circuit, which can be designed to realize any of the second-order functions.

#### KHN Biquad

Analyzed by superposition,

Where

Center frequency,

### Single Amplifier Biquadratic Active Filters

Single-amplifier biquads (*SABs*) are obtained by placing a bridged-T network in the negative-feedback path of an op amp. If the op amp is ideal, the poles realized are at the same locations as the zeros of the

#### Bridged T Amplifiers

### Sensitivity

The classical sensitivity function

## Signal Generators and Waveform-Shaping Circuits

There are two distinctly different types of signal generator: the linear oscillator, which utilizes some form of resonance, and the nonlinear oscillator or function generator, which employs a switching mechanism implemented with a multivibrator circuit.

### Oscillator Feedback loop

When an output signal is used as input into the

For a feedback loop to produce sinusoidal osciallations at frequency

This is the *Barkhausen criterion*.

When analyzing a given oscillator circuit, follow the following steps:

- Break the feedback loop to determine the loop gain
. - The oscillation frequency
is found as the frequency for which the phase angle of is zero or, equivalently, 360. - The condition for the oscillations to start is found from

#### Amplitude Control

A popular limiter circuit used to control the amplitude of oscillating circuits is pictured below. By disconnecting the feedback loop, the linear gain

#### Wien Bridge

### Bistable Multivibrators

A bistable multivibrator is an op amp circuit that switches between two stable states indefinitely when it receives a trigger signal.

The op amp will saturate at the value

From the transfer characteristics of the non-inverting feedback loop, we can derive this relationship:

When the

This pair of values in the negative and positive direction are the

For the non-inverting bistable circuit, superposition must be used to find the value of

To find the

This technique can be used to find the

For each case, adding a reference DC voltage

### Astable Multivibrators

By connecting a bistable multivibrator with an RC circuit in a feedback loop, a square wave can be generated where the circuit will switch states periodically. The capacitor will charge until it reaches

The time constant for this circuit is

### Monostable Multivibrator

A single pulse seen at point

After the period