### Logical Operation

The next few lessons go deep into electronics principles. We’ll be using some schematics to illustrate these circuits and their principles. To make your studies easier, know that only the schematics that have a figure number are on the exam. You’ll see those, like E7-1, come up in a later lesson.

In an earlier lesson, you learned about the different types of gates in a digital logic circuit. These included AND, NAND and NOR gates. There’s a way to keep track of all the potential changes and outputs you may have from these gates. It’s called a truth table. A truth table is **a list of inputs and corresponding outputs for a digital device** like these logic gates.

Let’s start with a truth table for a simple OR gate. An OR gate **produces 1 at its output if any input is 1****.** A truth table shows that any time input A or input B reads 1, the output reads 1.

Now let’s consider a NAND gate. The logical operation that a NAND (aka NOT AND) gate performs is that **it produces a 0 at its output only if all inputs are 1****.** Verify that on the truth table.

A two-input exclusive NOR gate **produces a 0 at its output if one and only one of its inputs is 1.**

Why do logic device designers use the terms Zero and 1 in a truth table? It’s called “positive logic.” **High voltage represents a 1, low voltage a 0.**

0 and 1 logic such as this can be integrated using a type of circuit called a multivibrator. A multivibrator is a simple 2 state circuit. It’s used for oscillators, timers and flip-flops. Multivibrators have three states:

**An astable multivibrator**is a circuit that continuously alternates between two states without an external clock. It constantly switches on and off. It’s unstable, making it an oscillator. Think of your car’s turn signals when they are engaged.- A monostable multivibrator
**switches temporarily to an alternate state for a set time.**It has one stable state, and one unstable state. Starting a timer would trigger the vibrator into an unstable state. When the vibrator returns to its stable state, the timer is complete. - A bistable multivibrator is either off or on. If that sounds like how computer memory works, go to the head of the class.

So, what does the schematic of a bistable multivibrator look like? One version is called **a flip-flop** circuit. That means that it is stable and can therefore be used to store state information. Each flip-flop can store one bit of data. Put millions and billions together and you have modern mass computer storage.

*Schematic of Flip-Flop circuit*

One important use of flip-flop circuits is a decade counter. A decade counter uses NAND gates in flip-flop circuits. It can track numbers, like a frequency display. An easy way to remember this is that on the calendar, a decade is 10 years.

*Schematic of a decade counter*

Flip-flop circuits are also used in frequency divider circuits. A frequency divider is used to generate lower frequencies in radios. Each **flip-flop** can divide the frequency of a pulse train by 2. If you wanted to divide a signal frequency by 16, then **4** flip-flops are required.

*Schematic of a frequency divider*

### Oscillator Circuits

Oscillator circuits are critical in amateur radio and all electronics. We know they create a periodic, oscillating signal. Oscillators in RF circuits produce sine wave signals. We then modulate the sine wave with the information we want the signal to carry. Think of the classic sine wave on a graph – this is created by an oscillating circuit.

There are three common types of oscillator circuits used in amateur radio gear. Those circuits are called: **Colpitts, Hartley and Pierce****.** You narrow down this answer to two choices on the exam. The correct answer only has one former president (Pierce) included in the list.

The Colpitts, Hartley and Pierce oscillators all use positive feedback. A positive feedback oscillator takes the output of the circuit and combines it back into the input. This “feedback loop” helps drive the oscillation of the circuit.

Each of the three uses a different mechanism for providing the positive feedback. Here’s a look:

In a Colpitts oscillator, the positive feedback is supplied **through a capacitive divider****.** You’ll see that as two capacitors near the output of the circuit.

In a Hartley oscillator, positive feedback is created through a tapped coil. You might find a Hartley or Colpitts oscillator in a VFO circuit. VFO stands for variable frequency oscillator. A VFO allows circuits to tune to a range of different frequencies.

The Pierce oscillator’s positive feedback is provided **through a quartz crystal****.** The schematic symbol for a crystal oscillator is labeled X.

A Pierce oscillator with its crystal can be a very accurate reference signal source. It’s frequently used in time circuits. Getting the crystal oscillator operating on the correct frequency specified by the manufacturer takes some circuit design. You must **provide the crystal with a specified parallel capacitance****.** This is shown in a schematic as two capacitors connected to ground.

The higher you move up the frequency bands, the greater the need becomes for stable oscillators. There are techniques for providing highly accurate and stable oscillators needed for microwave transmission and reception. They include:

- Use a GPS signal reference
- Use a rubidium stabilized reference oscillator or
- Use a temperature-controlled high Q dielectric resonator

**All these are correct** when asked about providing stable oscillators for microwave transmission.

One of the troubleshooting issues that occurs with oscillators is microphonics. That is **changes in oscillator frequency due to mechanical vibration****.** An oscillator’s microphonic responses can be reduced. To do that, **mechanically isolate the oscillator circuitry from its enclosure****.** Another issue for crystal oscillators is thermal drift. **NP0 capacitors** can be used to reduce it.