Logic Gates

Logic gates usually come packaged as integrated circuits which have type numbers such as 7400 or 4001.

They belong to semiconductor families such as TTL (transistor, transistor logic) or CMOS (complementary metal oxide semiconductor). The names describe their internal construction.

They are DIGITAL devices not ANALOGUE.

A thermometer is an analogue device because it can record an infinite number of values such 100 degrees, 0.1 degrees or 34.354 degrees etc.
Other analogue devices are a car speedo and a Hi Fi amplifier (which can handle lots of different frequencies and loudnesses.)

A digital device or system uses only two values. These can be expressed in several ways.

high or low
true or false
white or black
on or off
1 or 0

etc.

A light switch and a rat trap are digital devices.

Most gates usually have two or more inputs and one output.

The state of the output (high or low) depends upon the combination of the input states.

In the case of the gate shown, the output will only be high if both inputs are high. If either one input or both inputs are low then the output will be low

These characteristics can be shown using a TRUTH TABLE. In the following example 1 indicates a high and 0 indicates a low.
Note that Z is only a 1 when A AND B are both at 1.

There is a form of mathematics associated with logic gates called BOOLEAN ALGEBRA.
It was invented a few hundred years ago by Mr Boole, before the days of electronics. He used it to solve problems in logic.

For example
Some cats are black AND black items cannot be seen against a black wall.Therefore it is TRUE that some cats cannot be seen against a black wall.

Here is a Boolean expression for the gate shown. A . B = Z
Read this as IF A AND B ARE HIGH THEN Z IS HIGH. (The . is read as AND).

The most frequently used gates are AND, OR, NAND, NOR, NOT and EXOR.

An integrated circuit containing 4 AND gates each with 2 inputs is called a QUAD 2 INPUT AND ic. An ic with 6 NOT gates is called a HEX INVERTER ic.

Binary 7 Segment

Digital voltmeters, frequency counters etc use 7 segment displays to show the result of measurements.

However all the internal electronics use binary for manipulation of the data.

To convert this binary to a form that can be used by the display requires the use of a DECODER, in this case a "binary to 7 segment display decoder".

This has four inputs for the binary and seven outputs for the display.

Other types of decoder are available such as binary to decimal.

Operational Amplifier

The Basic Opamp

The opamp was originally designed to carry out mathematical operations in analogue computers, such as bombsights, but was soon recognised as having many other applications.

The opamp usually comes in the form of an 8 pin integrated circuit, the most common one being the type 741.
It has two inputs and one output.
The input marked with a - sign produces an amplified inverted output.
The input marked with a + sign produces an amplified but non inverted output.
The opamp requires positive and negative power supplies, together with a common ground.
Some circuits can be designed to work from a single supply.

If the two inputs are joined together, then the output voltage should be midway between the two supply rails, i.e. zero volts.
If it is not, then there are two connections for adding a potentiometer, to remove this OFFSET.

Opamp Characteristics

The opamp has a very high gain, typically (100 dB)100,000 times.

Looking at the left hand diagram, an input with a swing of a fraction of a millivolt produces an output that changes between + 12 volts and - 12 volts.
In most cases this gain is excessive, and is reduced by negative feed back.
Looking at the right hand diagram we can see that the opamp amplifies right down to dc.
Gain falls quite rapidly as the frequency increases.
In fact the bandwidth (the point at which the output has fallen by 3 dB) is only 1 kHz.
This is also improved upon by the use of negative feedback.
The input impedance is high, 1M.
The output impedance is low, 150 ohms.

Setting Opamp Gain

The gain of the inverting amplifier is determined by the feedback resistor R2, and the input resistor R1.
To minimize temperature drift, R3 is given the value of R1 and R2 in parallel.

Unity Gain Non Inverter

This non inverting amplifier has unity gain i.e. x1.
It is called a VOLTAGE FOLLOWER.
It serves the same purpose as the emitter follower.
It has a high input impedance and a very low output impedance.
It can be used for impedance matching.
It is able to drive several loads.

Non Inverter with Gain

Gain is 1+ R2/R1

Comparator

A varying input voltage is compared with a fixed reference voltage.
If the input voltage is higher than the reference voltage, then the output is negative.
If the input voltage is lower than the reference, then the output is positive.
The gain can be set by negative feedback.

Temperature Alarm

This circuit is configured as a comparator.
R1 and R2 provide a fixed reference voltage at the non inverting input.
The inverting input voltage is set by the other two resistors.
If the voltage at the inverting input rises above the reference voltage, then the the output goes to minus 12 volts and the buzzer is energised.
The behaviour of the circuit can be changed by swapping the preset and temperature dependent resistors.
Light dependent resistors etc can replace the temperature dependent one.

Opamp as a Timer

At switch on, the voltage across the capacitor is zero and the output is at +12 volts.
The buzzer is not energised.
After a time, determined by the values of C and R3, the voltage of the inverting input rises above that of the non inverting input.
The output goes to minus 12 volts and the buzzer is energised.

Opamp as an Audio Mixer



Opamp Dual Power Supplies

Most opamp circuits require two differing polarity voltages.
The upper diagram shows how the two supplies are connected together.
The bottom diagram shows how the common lead of the power supplies is connected to the input and output (and the common connection of any other associated circuitry).

NOR Gate Flip-Flop

Here, one input of each gate is held LOW by "pull down" resistors.

The other input is cross-coupled to the output of the other gate.

Initially, as shown in diagram A, gate 2 has two LOW inputs, so its output is HIGH.

This HIGH output is one input of gate 1, so the output of gate 1 is LOW.

When the SET input of gate 2 is momentarily pulsed HIGH, the output of gate 2 goes LOW.

This means that both inputs of gate 1 are LOW, so its output is HIGH, which is coupled to an input of gate 2.

Even though the pulse has finished, the output of gate 2 stays LOW because of this HIGH input.

The gates are now in the state shown in diagram B.

We say that the circuit has remembered or LATCHED and is in the SET state.

If the SET is pulsed again, nothing happens, the circuit stays in the SET state.

If the RESET on gate 1 is now pulsed HIGH, the output of gate 1 goes LOW.

This is coupled to gate 2 which now has two LOW inputs, so its output goes HIGH.

The gates have been RESET to their original states.

If the RESET is pulsed again, nothing happens, the circuit stays in the RESET state.

Note that when one output is HIGH, the other is LOW and vice-versa.

If both inputs are taken LOW simultaneously, then there is no change; both inputs are already LOW.

If both inputs are taken HIGH simultaneously, then the result is INDETERMINATE and is to be avoided.

A similar circuit can be constructed using nand gates and pull up resistors.

The inputs are pulsed low to change states.