# Passives

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## Capacitors

### Basics

You can think of a capacitor as sort of a rechargeable battery, connect it to a voltage and a current will flow into it charging it up, later it will have a voltage of its own that can push the current back out. The key equation for a capacitor is:

Where:

• C = capacitance ( units: farad = volts /coulomb )
• V = voltage ( unit: volts )
• Q = charge in the capacitor ( unit: coulomb )

A simple application of the formula above occurs when a constant or near constant current flow into a capacitor: then the voltage across it increases at a constant rate, the graph of the voltage against time will be a line rising ( or falling for a negative current ) from the left to the right. If the current is constant the line is straight.

Another way of thinking of a capacitor ( which is only partly correct ) is that it is a resistor with infinite resistance for DC and lower and lower resistance as the frequency goes up. This is a fair model for sinusoidal voltages and currents, but is less useful for signals such as square waves.

Uses:

• ac coupling –- blocking -- isolation
• timing
• Time for a capacitor to charge or discharge is very roughly RC where R is the resistor in series with the capacitor.
• Filter ( often power supply filter )
• decoupling
• tuned circuits

All capacitors are formed by having 2 conductors ( or plates ) connected to the two terminals of the capacitor. The conductors are separated from each other by insulator, typically very thin. Adding charge to one side forces like charge off the opposite plate because like charges repel. The larger the plates and the closer together they are the less voltage it takes to force in the charge. If the insulator ( called the dielectric ) is too thin it will be pierced by the charge and the capacitors becomes a conductor. Typically the basic specifications for a capacitors are its capacitance and the maximum voltage that can be used without causing the dialectic to break down.
There are many diferent technologies for manufacturing capacitor each with its own advantages and disadvantages.

### Electrolytic

In electrolytic capacitors the insulating layer is formed by electro chemical action between the plates and other chemicals in the capacitor. This forms a very thin layer which allows large capacitance in a small package. Typically this works for one polarity and not another so electrolytic capacitors are marked with their polarity. There are some non-polarized electrolytics, but they are not common.

## Inductors

An inductor reacts to current, but not to its value, but rather its change. It “tries” to keep the current through it constant. Any change in current causes a voltage across the inductor. The key equation for an inductor ( it is a bit complicated, but anyway here it ) is:

### equation here soon

where L = inductance ( units: henry ) V = voltage ( unit: volts ) I = current ( unit: Ampere ) t = time ( unit: seconds )

Uses:

• tuned circuits: a circuit that responds in a special way to some frequencies( s ).
• power supply filter: remove the pulsing DC left from rectification or other noise in the signal.
• Decoupling: usually blocking high frequencies from one part of a circuit from getting in another part.
• boost buck regulators: voltage regulators that decrease or increase voltage.

"Ferrites? I don't know much about 'em, I only use ferrites in switching regulators." --National Semiconductor's Bob Pease

Can be replaced in many circumstances with an impedance inverter using only an opamp, a capacitor, and a few resistors.

## Resistors

Probably the most basic component, just a hunk of wire ( low resistance ) or a long thin wire ( high resistance ).

When a voltage is applied to the two ends of an object, then a current usually flows through the object. If the object resists the voltage then the current will be small, if it does not then the current will be high. The amount of resistance is called ! The resistance. It is measured in ohms. ( Note that acting as a resistor is the simplest thing the object can do, there are more complicated behaviors, see capacitor, diodes, inductors, etc. A resistor is pretty much the simplest of electrical components. If almost no current flows we call the object an insulator, if a large current flows we call it a conductor. We often view a wire as a resistor of 0 ohms and an insulator as a resistor of infinite ohms. The key equation for a resistor is:

```R=V/I
```

where I = current ( unit: amperes, amps ) V = voltage ( unit: volts ) R = resistance ( unit: ohms = volts per amp )

List of standard 1% resistors. If you want 1% resistors, you must pick from this list or you will pay a fortune for the resistor, assuming you can ever get it. Interpret these numbers as the "mantissa" of the value. You can multiply the value by anything from 0.01 to about 100,000.

100 102 105 107 110 113 115 118 121 124 127 130 133 137 140 143 147 150 154 158 162 165 169 174 178 182 187 191 196 200 205 210 215 221 226 232 237 243 249 255 261 267 274 280 287 294 301 309 316 324 332 340 348 357 365 374 383 392 402 412 422 432 442 453 464 475 487 499 511 523 536 549 562 576 590 604 619 634 649 665 681 698 715 732 750 768 787 806 825 845 866 887 909 931 953 976

Uses

• current limiting:

Putting a resistor in a circuit, usually in series with another component it will reduce the current in the circuit, this is often useful to protect the other component. Very common to limit the current in a LED. current sense: When a resistor is in series with a circuit the voltage across it will vary with the current ( ohms law ) Sometimes we do this with a low value of resistance and use the voltage across the resistor to measure or control the current.

• Isolation :

A resistor between but connecting 2 components will tend to equalize their voltage, but only using small currents. It the components “want to go there own way, voltage wise” all they need do is put out a small current. For example people will sometimes ground themselves through a 10 mega ohm resistor. This tends to bring them to ground voltage, but they are protected from a deadly shock because most voltages cannot push a lethal current through 10 megs.

• pull up or pull down:

Sometimes a component will have a very high resistance to both the positive and negative side of the power supply and the voltage can easily drift around due to more or less random events. Under these conditions we will often connect a resistance ( typically around 10 K ohms ) to either the positive or negative side of the power supply. If to the positive side it is called a pull up resistor, if to the negative side a pull down resistor.

• voltage divider:

A voltage divider takes some voltage as an input and has an output that is some fraction of the input ( from 0 to 1 ) A volume control is usually some sort of voltage divider.

### Carbon

The most common found resistor is the carbor film. Theses are generally the cheapest and most used in devices. The commonly are designed to withstand 1/8, 1/4, 1/2, and 1 watts of power.

### Wire-Wound

Useful for cheap and accurate resistance, but has significant inductance compared to film resistors. Some may be wound in one direction, others half in one direction half in the other, this second method reduces but does not entirely eliminate the inductance. Very common in the range of 5 watts and up. Beware of these for use.

## Potentiometers

A Potentiometer is a resistor that has a third connection somewhere between the two main terminals. This connection is movable and if put at one end of the resistor will have no resistance between that end of the resistor and the full resistance to the other end. By moving the connection ( sometimes called a tap ) we can control the resistance to each end of the pot, but the sum of the two resistances always equals the total resistance of the potentiometer. A potentiometer is often used as a sort or adjustable voltage divider. There is an electriclly adjustable version: Digital_Potentiometers

Uses