3.3 Practical examples with coils and transformers

On the figure 2.6b coils, along with the capacitor, form two filters for conducting the currents to the speakers. The coil and capacitor C on figure 2.6c form a parallel oscillatory circuit for "amplifying" a particular radio signal, while rejecting all other frequencies.

Fig. 2.6: a. Amplifier with headphones, b. Band-switch, c. Detector radio-receiver

The most obvious application for a transformer is in a power supply. A typical transformer is shown in figure 3.8 and is used for converting 220V to 24V.

Fig. 3.8: Stabilized converter with circuit LM317

Output DC voltage can be adjusted via a linear potentiometer P, in 3~30V range.

Fig. 3.9: a. Stabilized converter with regulator 7806, b. auto-transformer, c. transformer for devices working at 110V, d. isolating transformer

Figure 3.9a shows a simple power supply, using a transformer with a centre-tap on the secondary winding. This makes possible the use two diodes instead of the bridge in figure 3.8.
Special types of transformers, mainly used in laboratories, are auto-transformers. The diagram for an auto-transformer is shown in figure 3.9b. It features only one winding, wound on an iron core. Voltage is taken from the transformer via a slider. When the slider is in its lowest position, voltage equals zero. Moving the slider upwards increases the voltage U, to 220V. Further moving the slider increases the voltage U above 220V.
The transformer in figure 3.9c converts 220v to 110v and is used for supplying devices designed to work on 110V.
As a final example, figure 3.9d represents an isolating transformer. This transformer features the same number of turns on primary and secondary windings. Secondary voltage is the same as the primary, 220V, but is completely isolated from the "mains," minimizing the risks of electrical shock. As a result, a person can stand on a wet floor and touch any part of the secondary without risk, which is not the case with the normal power outlet.

3.2.1 Working principles and basic characteristics

As already stated, transformers consist of two windings, primary and the secondary (figure 3.7). When the voltage Up is connected to the primary winding (in our case the "mains" is 220V), AC current Ip flows through it. This current creates a magnetic field which passes to the secondary winding via the core of the transformer, inducing voltage Us (24V in our example). The "load" is connected to the secondary winding, shown in the diagram as Rp (30Ω in our example). A typical load could be an electric bulb working at 24V with a consumption of 19.2W.

Fig. 3.7: Transformer: a. Working principles, b. Symbol

Transfer of electrical energy from the primary to the secondary is done via a magnetic field (called "flux") and a magnetic circuit called the "core of the transformer." To prevent losses, it is necessary to make sure the whole magnetic field created by the primary passes to the secondary. This is achieved by using an iron core, which has much lower magnetic resistance than air.
Primary voltage is the "mains" voltage. This value can be 220V or 110V, depending on the country. Secondary voltage is usually much lower, such as 6V, 9V, 15V, 24V, etc, but can also be higher than 220V, depending on the transformer's purpose. Relation of the primary and secondary voltage is given with the following formula:

where Ns and Np represent the number of turns on the primary and secondary winding, respectively. For instance, if Ns equals 80 and Np equals 743, secondary voltage will be:

Relationship between the primary and secondary current is determined by the following formula:

For instance, if Rp equals 30Ω, then the secondary current equals Ip = Up/Rp = 24V/30Ω = 0.8A. If Ns equals 80 and Np equals 743, primary current will be:

Transformer wattage can be calculated by the following formulae:

In our example, the power equals:

Everything up to this point relates to the ideal transformer. Clearly, there is no such thing as perfect, as losses are inevitable. They are present due to the fact that the windings exhibit a certain resistance value, which makes the transformer warm up during operation, and the fact that the magnetic field created by the primary does not entirely pass to the secondary. This is why the output wattage is less than the input wattage. Their ratio is called EFFICIENCY:

For transformers delivering hundreds of watts, efficiency is about µ=0.85, meaning that 85% of the electrical energy taken from the mains gets to the consumer, while the 15% is lost due to previously mentioned factors in the form of heat. For example, if power required by the consumer equals Up*Ip = 30W, then the power which the transformer draws from the maains equals:

To avoid any confusion here, bear in mind that manufacturers have already taken every measure in minimizing the losses of transformers and other electronic components and that, practically, this is the highest possible efficiency. When acquiring a transformer, you should only worry about the required voltage and the maximal current of the secondary. Dividing the wattage and the secondary voltage gets you the maximal current value for the consumer. Dividing the wattage and the primary voltage gets you the current that the transformer draws from network, which is important to know when buying the fuse. Anyhow, you should be able to calculate any value you might need using the appropriate formulae from above.

3.2 Transformers

For electronic devices to function it is necessary to have a DC power supply. Batteries and rechargeable cells can fulfill the role, but a much more efficient way is to use a POWER SUPPLY. The basic component of a power supplyr is a transformer to transform the 220V "mains" to a lower value, say 12V. A common type of transformer has one primary winding which connects to the 220V and one (or several) secondary windings for the lower voltages. Most commonly, cores are made of E and I laminations, but some are made of ferromagnetic material. There are also iron core transformers used for higher frequencies. Various types of transformers are shown on the picture below.

Fig. 3.5: Various types of transformers

Symbols for a transformer are shown on the figure 3.6 Two vertical lines indicate that primary and secondary windings share the same core.

Fig. 3.6: Transformer symbols

With the transformer, manufacturers usually supply a diagram containing information about the primary and secondary windings, the voltages and maximal currents. In the case where the diagram is missing, there is a simple method for determining which winding is the primary and which is the secondary: a primary winding consists of thinner wire and more turns than the secondary. It has a higher resistance - and can be easily be tested by ohmmeter. Figure 3.6d shows the symbol for a transformer with two independent secondary windings, one of them has three tappings, giving a total of 4 different output voltages. The 5v secondary is made of thinner wire with a maximal current of 0.3A, while the other winding is made of thicker wire with a maximal current of 1.5A. Maximum voltage on the larger secondary is 48V, as shown on the figure. Note that voltages other than those marked on the diagram can be produced - for example, a voltage between tappings marked 27V and 36V equals 9V, voltage between tappings marked 27V and 42V equals 15V, etc.

3.1 Coils

Coils are not a very common component in electronic circuits, however when they are used, they need to be understood. They are encountered in oscillators, radio-receivers, transmitter and similar devices containing oscillatory circuits. In amateur devices, coils can be made by winding one or more layers of insulated copper wire onto a former such as PVC, cardboard, etc. Factory-made coils come in different shapes and sizes, but the common feature for all is an insulated body with turns of copper wire.
The basic characteristic of every coil is its inductance. Inductance is measured in Henry (H), but more common are millihenry (mH) and microhenry (µH) as one Henry is quite a high inductance value. As a reminder:

1H = 1000mH = 106 µH

Coil inductance is marked by XL, and can be calculated using the following formula:

where f represents the frequency of the voltage in Hz and the L represents the coil inductance in H.
For example, if f equals 684 kHz, while L=0.6 mH, coil impedance will be:The same coil would have three times higher impedance at three times higher frequency. As can be seen from the formula above, coil impedance is in direct proportion to frequency, so that coils, as well as capacitors, are used in circuits for filtering at specified frequencies. Note that coil impedance equals zero for DC (f=0).
Several coils are shown on the figures 3.1, 3.2, 3.3, and 3.4.
The simplest coil is a single-layer air core coil. It is made on a cylindrical insulator (PVC, cardboard, etc.), as shown in figure 3.1. In the figure 3.1a, turns have space left between them, while the common practice is to wind the wire with no space between turns. To prevent the coil unwinding, the ends should be put through small holes as shown in the figure.

Fig. 3.1: Single-layer coil

Figure 3.1b shows how the coil is made. If the coil needs 120 turns with a tapping on the thirtieth turn, there are two coils L1 with 30 turns and L2 with 90 turns. When the end of the first and the beginning of the second coil are soldered, we get a "tapping."
A multilayered coil is shown in figure 3.2a. The inside of the plastic former has a screw-thread, so that the ferromagnetic core in the shape of a small screw can be inserted. Screwing the core moves it along the axis and into the center of the coil to increase the inductance. In this manner, fine changes to the inductance can be made.

Fig. 3.2: a. Multi-layered coil with core, b. Coupled coils

Figure 3.2b shows a high-frequency transformer. As can be seen, these are two coils are coupled by magnetic induction on a shared body. When the coils are required to have exact inductance values, each coil has a ferromagnetic core that can be adjusted along the coil axis.
At very high frequencies (above 50MHz) coil inductance is small, so coils need only a few turns. These coils are made of thick copper wire (approx. 0.5mm) with no coil body, as shown on the figure 3.3a. Their inductance can be adjusted by physically stretching or squeezing the turns together.

Fig. 3.3: a. High frequency coil, b. Inter-frequency transformer

Figure 3.3b shows a metal casing containing two coils, with the schematic on the right. The parallel connection of the first coil and capacitor C forms an oscillatory circuit. The second coil is used for transferring the signal to the next stage. This is used in radio-receivers and similar devices. The metal casing serves as a screen to prevent external signals affecting the coils. For the casing to be effective, it must be earthed.
Fig 3.4 shows a "pot core" inductor. The core is made in two halves and are glued together. The core is made of ferromagnetic material, commonly called "ferrite." These inductors are used at frequencies up to 100kHz. Adjustment of the inductance can be made by the brass or steel screw in the centre of the coil.

Fig. 3.4: A "pot core" inductor

3. Coils and transformers

Coils are not a very common component in electronic circuits, however when they are used, they need to be understood. They are encountered in oscillators, radio-receivers, transmitter and similar devices containing oscillatory circuits. In amateur devices, coils can be made by winding one or more layers of insulated copper wire onto a former such as PVC, cardboard, etc. Factory-made coils come in different shapes and sizes, but the common feature for all is an insulated body with turns of copper wire.

For electronic devices to function it is necessary to have a DC power supply. Batteries and rechargeable cells can fulfill the role, but a much more efficient way is to use a POWER SUPPLY. The basic component of a power supplyr is a transformer to transform the 220V "mains" to a lower value, say 12V. A common type of transformer has one primary winding which connects to the 220V and one (or several) secondary windings for the lower voltages. Most commonly, cores are made of E and I laminations, but some are made of ferromagnetic material. There are also iron core transformers used for higher frequencies. Various types of transformers are shown on the picture below.

2.4 Practical examples

Several practical examples using capacitors are shown in photo 1. A 5µF electrolytic capacitor is used for DC blocking. It allows the signal to pass from one sage to the next while prevent the DC on one stage from being passed to the next stage. This occurs because the capacitor acts like a resistor of very low resistance for the signals and as a resistor of high resistance for DC.

photo 1 : a. Amplifier with headphones, b. Electrical band-switch

The photo 1.b represents a diagram of a band-switch with two speakers, with Z1 used for reproducing low and mid-frequency signals, and Z2 for high frequency signals. 1 and 2 are connected to the audio amplifier output. Coils L1 and L2 and the capacitor C ensure that low and mid-frequency currents flow to the speaker Z1, while high frequency currents flow to Z2. How this works exactly ? In the case of a high frequency current, it can flow through either Z1 and L1 or Z2 and C. Since the frequency is high, impedance (resistance) of the coils are high, while the capacitor's reactance is low. It is clear that in this case, current will flow through Z2. In similar fashion, in case of low-frequency signals, current will flow through Z1, due to high capacitor reactance and low coil impedance.

photo 1 : c. Detector radio-receiver

The photo 1.c represents a circuit diagram for a simple detector radio-receiver (commonly called a "crystal set"), where the variable capacitor C, forming the oscillatory circuit with the coil L, is used for frequency tuning. Turning the capacitor's rotor changes the resonating frequency of the circuit, and when matching a certain radio frequency, the station can be heard.

2.3 Variable capacitors

Variable capacitors are capacitors with variable capacity. Their minimal capacity ranges from 1p and their maximum capacity goes as high as few hundred pF (500pF max). Variable capacitors are manufactured in various shapes and sizes, but common features for them is a set of fixed plates (called the stator) and a set of movable plates. These plates are fitted into each other and can be taken into and out of mesh by rotating a shaft. The insulator (dielectric) between the plates is air or a thin layer of plastic, hence the name variable capacitor. When adjusting these capacitors, it is important that the plates do not touch.

Below are photos of air-dielectric capacitors as well as mylar-insulated variable capacitors (photo 1-a).

photo 1 : a, b, c. Variable capacitors, d. Trimmer capacitors

The first photo shows a "ganged capacitor" in which two capacitors are rotated at the same time. This type of capacitor is used in radio receivers. The larger is used for the tuning circuit, and the smaller one in the local oscillator. The symbol for these capacitors is also shown in the photo.
Beside capacitors with air dielectric, there are also variable capacitors with solid insulator. With these, thin insulating material such as mylar occupies the space between stator and rotor. These capacitors are much more resistant to mechanical damage. They are shown in photo 1-b.
The most common devices containing variable capacitors are radio receivers, where these are used for frequency adjustment. Semi-variable or trim capacitors are miniature capacitors, with capacity ranging from several pF to several tens of pFs. These are used for fine tuning radio receivers, radio transmitters, oscillators, etc. Three trimmers, along with their symbol, are shown on the photo 1-d.

2.2 Electrolytic capacitors

Electrolytic capacitors represent the special type of capacitors with fixed capacity value. Thanks to special construction, they can have exceptionally high capacity, ranging from one to several thousand µF. They are most frequently used in circuits for filtering, however they also have other purposes.
Electrolytic capacitors are polarized components, meaning they have positive and negative leads, which is very important when connecting it to a circuit. The positive lead or pin has to be connected to the point with a higher positive voltage than the negative lead. If it is connected in reverse the insulating layer inside the capacitor will be "dissolved" and the capacitor will be permanently damaged.
Explosion may also occur if capacitor is connected to voltage that exceeds its working voltage. In order to prevent such instances, one of the capacitor's connectors is very clearly marked with a + or -, while the working voltage is printed on the case.
Several models of electrolytic capacitors, as well as their symbols, are shown on the picture below.

photo 1 : Electrolytic capacitors

Tantalum capacitors represent a special type of electrolytic capacitor. Their parasitic inductance is much lower than standard aluminum electrolytic capacitors so that tantalum capacitors with significantly (even ten times) lower capacity can completely substitute an aluminum electrolytic capacitor.

2.1.1 Marking the block-capacitors

Commonly, capacitors are marked by a set of numbers representing the capacity. Beside this value is another number representing the maximal working voltage, and sometimes tolerance, temperature coefficient and some other values are printed as well. But on the smallest capacitors (such as surface-mount) there are no markings at all and you must not remove them from their protective strips until they are needed. The size of a capacitor is never an indication of its value as the dielectric and the number of layers or "plates" can vary from manufacturer to manufacturer. The value of a capacitor on a circuit diagram, marked as 4n7/40V, means the capacitor is 4,700pF and its maximal working voltage is 40v. Any other 4n7 capacitor with higher maximal working voltage can be used, but they are larger and more expensive.
Sometimes, capacitors are identified with colors, similar to the 4-band system used for resistors (photo 1). The first two colors (A and B) represent the first two digits, third color (C) is the multiplier, fourth color (D) is the tolerance, and the fifth color (E) is the working voltage.
With disk-ceramic capacitors (photo 1 -b) and tubular capacitors (photo 1 -c) working voltage is not specified, because these are used in circuits with low DC voltage. If a tubular capacitor has five color bands on it, the first color represents the temperature coefficient, while the other four specify the capacity in the previously described way.

photo 1 : Marking the capacity using colors

The photo 2 shows how the capacity of miniature tantalum electrolytic capacitors are marked by colors. The first two colors represent the first two digits and have the same values as with resistors. The third color represents the multiplier, to get the capacity expressed in µF. The fourth color represents the maximal working voltage.

photo 2 : Marking the tantalum electrolytic capacitors

One important note on the working voltage: The voltage across a capacitor must not exceed the maximal working voltage as the capacitor may get destroyed. In the case when the voltage is unknown, the "worst" case should be considered. There is the possibility that, due to malfunction of some other component, the voltage on capacitor equals the power supply voltage. If, for example, the supply is 12V, the maximal working voltage for the capacitor should be higher than 12V.

2.1 Block-capacitors

Capacitors with fixed values (the so called block-capacitors) consist of two thin metal plates (these are called "electrodes" or sometimes called the "foil"), separated by a thin insulating material such as plastic. The most commonly used material for the "plates" is aluminum, while the common materials used for insulator include paper, ceramic, mica, etc after which the capacitors get named. A number of different block-capacitors are shown in the photo below. A symbol for a capacitor is in the upper right corner of the image.

Block capacitors

Most of the capacitors, block-capacitors included, are non-polarized components, meaning that their leads are equivalent in respect of the way the capacitor can be placed in a circuit. Electrolytic capacitors represent the exception as their polarity is important. This will be covered in the following chapters.

2. Capacitors

Capacitors are common components of electronic circuits, used almost as frequently as resistors. The basic difference between the two is the fact that capacitor resistance (called reactance) depends on the frequency of the signal passing through the item. The symbol for reactance is Xc and it can be calculated using the following formula:

f representing the frequency in Hz and C representing the capacitance in Farads.
For example, 5nF-capacitor's reactance at f=125kHz equals: while, at f=1.25MHz, it equals:A capacitor has an infinitely high reactance for direct current, because f=0.
Capacitors are used in circuits for many different purposes. They are common components of filters, oscillators, power supplies, amplifiers, etc.
The basic characteristic of a capacitor is its capacity - the higher the capacity, the higher is the amount of electricity it can hold. Capacity is measured in Farads (F). As one Farad represents fairly high capacity, smaller values such as microfarad (µF), nanofarad (nF) and picofarad (pF) are commonly used. As a reminder, relations between units are:
1F=106µF=109nF=1012pF,
that is 1µF=1000nF and 1nF=1000pF. It is essential to remember this notation, as same values may be marked differently in some circuits. For example, 1500pF is the same as 1.5nF, 100nF is 0.1µF. A simpler notation system is used as with resistors. If the mark on the capacitor is 120 the value is 120pF, 1n2 stands for 1.2nF, n22 stands for 0.22nF, while .1µ (or .1u) stands for 0.1µF.
Capacitors come in various shapes and sizes, depending on their capacity, working voltage, type of insulation, temperature coefficient and other factors. All capacitors can divided in two groups: those with changeable capacity values and those with fixed capacity values. These will covered in the following chapters.

1.6 Practical examples with potentiometers

As previously stated, potentiometers are most commonly used in amps, radio and TV receivers, cassette players and similar devices. They are used for adjusting volume, tone, balance, etc.
As an example, we will analyze the common circuit for tone regulation in an audio amp. It contains two pots and is shown in the photo 1.

photo 1 : Tone regulation circuit: a. Electrical scheme, b. Function of amplification

Potentiometer marked BASS regulates low frequency amplification. When the slider is in the lowest position, amplification of very low frequency signals (tens of Hz) is about ten times greater than the amplification of mid frequency signals (~kHz). If slider is in the uppermost position, amplification of very low frequency signals is about ten times lower than the amplification of mid frequency signals. Low frequency boost is useful when listening to music with a beat (disco, jazz, R&B...), while Low Frequency amplification should be reduced when listening to speech or classical music.
Similarly, potentiometer marked TREBLE regulates high frequency amplification. High frequency boost is useful when music consists of high-pitched tones such as chimes, while for example High Frequency amplification should be reduced when listening to an old record to reduce the background noise.
Diagram 1 shows the function of amplification depending upon the signal frequency. If both sliders are in their uppermost position, the result is shown with curve 1-2. If both are in mid position function is described with line 3-4, and with both sliders in the lowest position, the result is shown with curve 5-6. Setting the pair of sliders to any other possible results in curves between curves 1-2 and 5-6.

Potentiometers BASS and TREBLE are coated by construction and linear by resistance.
The third pot in the diagram is a volume control. It is coated and logarithmic by resistance (hence the mark log)

1.5 Potentiometers

Potentiometers (also called pots) are variable resistors, used as voltage or current regulators in electronic circuits. By means of construction, they can be divided into 2 groups: coated and wire-wound.
With coated potentiometers, (photo 1), insulator body is coated with a resistive material. There is a conductive slider moving across the resistive layer, increasing the resistance between slider and one end of pot, while decreasing the resistance between slider and the other end of pot.

photo 1 : Coated potentiometer

Wire-wound potentiometers are made of conductor wire coiled around insulator body. There is a slider moving across the wire, increasing the resistance between slider and one end of pot, while decreasing the resistance between slider and the other end of pot.
Coated pots are much more common. With these, resistance can be linear, logarithmic, inverse-logarithmic or other, depending upon the angle or position of the slider. Most common are linear and logarithmic potentiometers, and the most common applications are radio-receivers, audio amplifiers, and similar devices where pots are used for adjusting the volume, tone, balance, etc.
Wire-wound potentiometers are used in devices which require more accuracy in control. They feature higher dissipation than coated pots, and are therefore in high current circuits.
Potentiometer resistance is commonly of E6 series, including the values: 1, 2.2 and 4.7. Standard tolerance values include 30%, 20%, 10% (and 5% for wire-wound pots).
Potentiometers come in many different shapes and sizes, with wattage ranging from 1/4W (coated pots for volume control in amps, etc) to tens of watts (for regulating high currents). Several different pots are shown in the photo 2, along with the symbol for a potentiometer.

photo 2 : Potentiometers

The upper model represents a stereo potentiometer. These are actually two pots in one casing, with sliders mounted on shared axis, so they move simultaneously. These are used in stereophonic amps for simultaneous regulation of both left and right channels, etc.
Lower left is the so called slider potentiometer.
Lower right is a wire-wound pot with a wattage of 20W, commonly used as rheostat (for regulating current while charging a battery etc).
For circuits that demand very accurate voltage and current values, trimmer potentiometers (or just trim pots) are used. These are small potentiometers with a slider that is adjusted via a screwdriver.
Trim pots also come in many different shapes and sizes, with wattage ranging from 0.1W to 0.5W. photo 3 shows several different trim pots, along with the symbol.

photo 3 : Trim pots

Resistance adjustments are made via a screwdriver. Exception is the trim pot on the lower right, which can be adjusted via a plastic shaft. Particularly fine adjusting can be achieved with the trim pot in the plastic rectangular casing (lower middle). Its slider is moved via a screw, so that several full turns is required to move the slider from one end to the other.

1.4 Practical examples with resistors

shows two practical examples with nonlinear and regular resistors as trimmer potentiometers, elements which will be covered in the following chapter.

photo 1 : RC amplifier

represents an RC voltage amplifier, that can be used for amplifying low-frequency, low-amplitude audio signals, such as microphone signals. The signal to be amplified is brought between node 1 (amplifier input) and gnd, while the resulting amplified signal appears between node 2 (amplifier output) and gnd. To get the optimal performance (high amplification, low distortion, low noise, etc) , it is necessary to "set" the transistor's operating point. Details on the operating point will be provided in chapter 4; for now, let's just say that DC voltage between node C and gnd should be approximately one half of battery (power supply) voltage. Since battery voltage equals 6V, voltage in node C should be set to 3V. Adjustments are made via resistor R1.

Connect a voltmeter between node C and gnd. If voltage exceeds 3V, replace the resistor R1=1.2MW with a smaller resistor, say R1=1MW. If voltage still exceeds 3V, keep lowering the resistance until it reaches approximately 3V. If the voltage at node C is originally lower than 3V, increase the resistance of R1.

The degree of amplification of the stage depends on R2 resistance: higher resistance - higher amplification, lower resistance - lower amplification. If the value of R2 is changed, the voltage at node C should be checked and adjusted (via R1).

Resistor R3 and 100µF capacitor form a filter to prevent feedback from occurring. This feedback is called "Motor-boating" as it sounds like the noise from a motor-boat. This noise is only produced when more than one stage is employed. As more stages are added to a circuit, the chance of feedback, in the form of instability or motor-boating, will occur. This noise appears at the output of the amplifier, even when no signal is being delivered to the amplifier. The instability is produced in the following manner:Even though no signal is being delivered to the input, the output stage produces a very small background noise called "hiss. This comes from current flowing through the transistors and other components. This puts a very small waveform on the power rails. This waveform is passed to the input of the first transistor and thus we have produced a loop for "noise-generation." The speed with which the signal can pass around the circuit determines the frequency of the instability. By adding a resistor and electrolytic to each stage, a low-frequency filter is produced and this "kills" or reduces the amplitude of the offending signal. The value of R3 can be increased if needed.

Practical examples with resistors will be covered in the following chapters as almost all circuits require resistors.

photo 2 : Sound indicator of changes in temperature or the amount of light

A practical use for nonlinear resistors is illustrated on a simple alarm device shown in figure 1.5b. Without trimmer TP and nonlinear NTC resistor it is an audio oscillator. Frequency of the sound can be calculated according to the following formula:

photo 3

In our case, R=47kW and C=47nF, and the frequency equals:

photo 4

When, according to the figure, trim pot and NTC resistor are added, oscillator frequency increases. If the trim pot is set to minimum resistance, the oscillator stops. At the desired temperature, the resistance of the trim pot should be increased until the oscillator starts working again. For example, if these settings were made at 2°C, the oscillator remains frozen at higher temperatures, as the NTC resistor's resistance is lower than nominal. If the temperature falls the resistance increases and at 2°C the oscillator is activated.
If an NTC resistor is installed in a car, close to the road surface, the oscillator can warn driver if the road is covered with ice. Naturally, the resistor and two copper wires connecting it to the circuit should be protected from dirt and water.
If, instead of an NTC resistor, a PTC resistor is used, the oscillator will be activated when the temperature rises above a certain designated value. For example, a PTC resistor could be used for indicating the state of a refrigerator: set the oscillator to work at temperatures above 6°C via trimmer TP, and the circuit will signal if anything is wrong with the fridge.
Instead of an NTC, we could use an LDR resistor - the oscillator would be blocked as long as a certain amount of light is present. In this way, we could make a simple alarm system for rooms where a light must be always on.
The LDR can be coupled with resistor R. In that case, the oscillator works when the light is present, otherwise it is blocked. This could be an interesting alarm clock for huntsmen and fishermen who would like to get up at the crack of dawn, but only if the weather is clear. For the desired moment in the early morning, the trim pot should be set to the uppermost position. Then, the resistance should be carefully reduced, until the oscillator starts. During the night the oscillator will be blocked, since there is no light and LDR resistance is very high. As the amount of light increases in the morning, the resistance of the LDR drops and the oscillator is activated when the LDR is illuminated with the required amount of light.
The trim pot from the figure 1.5b is used for fine adjustments. Thus, TP from figure 1.5b can be used for setting the oscillator to activate under different conditions (higher or lower temperature or amount of light).

1.3 Nonlinear resistors

Resistance values detailed above are a constant and do not change if the voltage or current-flow alters. But there are circuits that require resistors to change value with a change in temperate or light. This function may not be linear, hence the name NONLINEAR RESISTORS.

There are several types of nonlinear resistors, but the most commonly used include : NTC resistors (figure a) (Negative Temperature Co-efficient) - their resistance lowers with temperature rise. PTC resistors (figure b) (Positive Temperature Co-efficient) - their resistance increases with the temperature rise. LDR resistors (figure c) (Light Dependent Resistors) - their resistance lowers with the increase in light. VDR resistors (Voltage dependent Resistors) - their resistance critically lowers as the voltage exceeds a certain value. Symbols representing these resistors are shown below.

photo 1 : Nonlinear resistors - a. NTC, b. PTC, c. LDR

In amateur conditions where nonlinear resistor may not be available, it can be replaced with other components. For example, NTC resistor may be replaced with a transistor with a trimmer potentiometer, for adjusting the required resistance value. Automobile light may play the role of PTC resistor, while LDR resistor could be replaced with an open transistor. As an example, figure on the right shows the 2N3055, with its upper part removed, so that light may fall upon the crystal inside.

photo 2

1.2 Resistor Dissipation

If the flow of current through a resistor increases, it heats up, and if the temperature exceeds a certain critical value, it can be damaged. The wattage rating of a resistor is the power it can dissipate over a long period of time. Wattage rating is not identified on small resistors. The following diagrams show the size and wattage rating:

photo 1 Resistor dimensions

Most commonly used resistors in electronic circuits have a wattage rating of 1/2W or 1/4W. There are smaller resistors (1/8W and 1/16W) and higher (1W, 2W, 5W, etc). In place of a single resistor with specified dissipation, another one with the same resistance and higher rating may be used, but its larger dimensions increase the space taken on a printed circuit board as well as the added cost.

Power (in watts) can be calculated according to one of the following formulae, where U is the symbol for Voltage across the resistor (and is in Volts), I is the symbol for Current in Amps and R is the resistance in ohms:

photo 2

For example, if the voltage across an 820W resistor is 12V, the wattage dissipated by the resistors is:

photo 3

A 1/4W resistor can be used.

In many cases, it is not easy to determine the current or voltage across a resistor. In this case the wattage dissipated by the resistor is determined for the "worst" case. We should assume the highest possible voltage across a resistor, i.e. the full voltage of the power supply (battery, etc). If we mark this voltage as VB, the highest dissipation is:

photo 4

For example, if VB=9V, the dissipation of a 220W resistor is:

photo 5

A 0.5W or higher wattage resistor should be used