Ohms’ Law in Basic DC Electronic Circuit Design

This is a revised and hitherto unpublished transcript, adapted to be converted to .pdf format as an eBook, which differs slightly from the original at the end only.

The content is very much the same as the original.

 

 

Foreword

Electronics is a vast and complicated field. There’s so much to learn, and that learning curve never stops. No matter how much you know; there’s always more to be known as new discoveries are constantly being made.

For instance; forty years ago, nobody would have thought that the recently-invented transistor would be at the centre of technological advancement. It would have been thought of as a crazy notion that over sixty million transistors could be compacted into a device with the volume of a standard matchbox that is the central processing unit of a powerful personal computer.

 

In those days the dominant technology was the thermionic valve or vacuum tube. The operation of these devices is, in a way, similar to that of a transistor; the problem being that high voltages are required in the associated circuitry before they will function. Also the cathode or negative electrode of every thermionic valve needs to be kept red hot, in order for the high voltage electricity to flow through the device. This required a separate low-voltage supply to power the heater, in addition to anything else. Although it became possible eventually to incorporate up to three separate valves into a single vacuum tube; that was about the limit as far as that technology was concerned at the time.

 

I’ll be taking you through a very basic but in-depth look at the basics of DC electronic circuit design using Ohm’s Law. You won’t be a genius when you’ve read it, neither will you have enough knowledge to become a technician. At the end of it you’ll be able to design a very simple bipolar transistor circuit using resistors and a transistor, and you’ll know how voltage, DC electrical resistance, amperage, and wattage, are interrelated by Ohm’s Law.

You’ll be able to calculate the resistance in Ohms of any resistance load in a DC circuit simply by measuring the current passing through it as well as the voltage potential across the load. You’ll know how to set the voltage of the centre-point of a potential divider by choosing different values of resistor, as well as how to amplify a DC voltage using a transistor: All this is made possible by Ohm’s Law.

In this book I’m not intending to describe in great detail the various functions of individual electronic components. Where this may be necessary I’ve linked to articles containing further information on the subject, should the reader require it.

This book is mainly about calculation used in simple circuit design, brought about by the use of basic calculus, in part using Ohms’ Law . A knowledge of component identification and function is assumed in the reader. If this happens to not be the case then the information provided at the destination of the links incorporated within the text should be a sufficient source of this knowledge.

The book that you’re now reading does not endeavour to go into digital electronics, and concentrates rather on basic analogue DC circuit principles, which should be learned as a forerunner to the discovery of digital circuitry.

Electronics is a very intense subject with a great deal of depth; and one could devote one’s entire lifetime to the furtherance of knowledge in this field. However with the rate of new discoveries now being made it is extremely unlikely that one could ever learn everything there is to know about the subject in even a very long lifetime.

This book is intended for the beginner. However, by utilising the links provided I feel even an absolute beginner would be able to keep up, with much study, and progress a certain amount whilst doing so.

 

 

_._

Georg Simon Ohm was born in Germany on 16th March 1789, and lived until 6 July 1854. He became a physicist, and during his career determined that there is a direct proportionality between the voltage applied across a conductor and the resultant electric current flowing in the circuit. Further experimentation meant that eventually Ohm was able to define the relationships of voltage, current, and electrical resistance.

 

The unit of electrical resistance; the OHM (Symbolised by the Greek letter Omega.), was named after Georg Simon Ohm in his honour

_._

In this book I’m going to be using circuit diagrams and circuit-diagrammatical symbols. For those not familiar with circuit diagrams I would suggest that you take a look at this link or here to familiarise yourself with some of the symbols used. You will notice that I don’t always stick to the usual format in a number of cases when I’m drawing my own circuit diagrams freehand: For instance; when I’m drawing a resistor I use a diagonal zig-zag line rather than a rectangular box. Also when drawing a transistor symbol I usually omit the circle around the device.

This is for a number of purposes; the main ones being speed and neatness: If you’ve ever tried to draw a perfect circle without using a pair of compasses or a jar lid, you’ll know just how difficult it is. The symbol inside the circle is the same and unique whichever way round one draws it. The reason for the circle is to indicate that the device is a discreet device, meaning a single device in a package; as opposed to a multi-transistor on a chip or an integrated circuit. For this article we’ll just use the symbol without the circle: It’s a transistor and that’s that.

 

 

Standard Transistor Symbol     Transistor Symbol Used Herein

 

 

(The link shows only the symbols of a bipolar NPN and a PNP transistor, and also a phototransistor. There are many other types of transistor; such as the FET or Field Effect Transistor in its various different guises. (Which, incidentally, was not named after the author; Sharron Field. (Sadly.))

As I stated earlier, I use the zig-zag line as the symbol for a resistor. This was once the standard symbol for a resistor. It was partially abandoned for the sake of clarity because it looks too similar to the symbol for an inductor , the symbol of which has curves where the old resistor symbol has angles.

 

= This is how I draw a resistor

 

Whereas this is the modern standard symbol:

 

I personally use the old zig-zag line symbol because it’s vastly easier to draw and takes less than 1/4 of the time. If I try to draw a rectangular box I end up wishing I hadn’t, as it usually looks by no means rectangular.

You’ll notice that the circuit diagrams that I’ve included were drawn with a pen or pencil on paper and scanned in: That’s the way things are currently. I don’t at the moment have either the software to draw exclusively on the computer nor the time and patience to learn how to use it. The situation may be different in the future; but right now that’s the way things stand.

 

Let’s start by taking a look at the very basic basics of Ohm’s Law: -

 

The Basic Triangle

So let’s look at the most basic bit of Ohm’s Law first; that being the relationship of Voltage to current to resistance in a DC (Direct Current) environment: -

The relationship can be expressed in an easy-to-remember format thus:

 

V

I        R

Where V is Voltage in Volts,

I is electric_current in Amperes,

and R is DC electrical resistance in Ohms

 

 

From this simple illustration we can draw the following equations:-

 

V / I = R

V / R = I

I x R = V

 

If we were to substitute the figure 1 for all of the variables we would notice that the equations are all true and equal in their most basic form: If a single Ampere flowed through a resistance of a single ohm at a voltage of a single volt it would be the point of nearest correlation between the three measurements.

If, as happens in nearly all cases in a practical working environment, we were to a increase or decrease the value to a number less than or greater than one for any or all of these variables, then that correlation vanishes; yet the equations still hold together.

 

Let’s look at an example: -

 

A current of 2 Amperes, or amps for short, is flowing through a resistance of 2 Ohms.

In this case Ohm’s law tells us that the voltage present at the point where the current exits the 2 Ohm resistor is 4 Volts; as 2 amps x 2 Ohms = 4 Volts.

 

Another example: –

An unspecified current is flowing through a resistance of 10 Ohms. The voltage at the point where the current exits the resistor is 5 Volts.

Ohms’ Law reveals that the unspecified current must be 5 Volts / 10 Ohms = 1/2 amp.

 

A third example: -

A current of 0.1 amps, or 100 milliamps, is outputting a resistor at a Voltage of 0.3 Volts, or 300 millivolts.

Ohms’ Law informs us that the resistor’s value in Ohms is 0.3 Volts / 0.1 amps = 3 Ohms.

Yes it really is that simple; at least at this stage in the proceedings.

 

Power

The next denomination we introduce into the mix is electrical power, represented by the letter P; and which is measured in Watts. here; another law, that being Joule’s Law, which is named after the British physicist James Joule.

Joules’ Law has 2 main equations for giving the relation of power, or wattage, to the integers that we’ve already introduced in Ohms’ Law: The following equations describe this relationship: -

P = I x V

                  

            2   ,                                                               

P = V  / I       (P = V squared / square root of I)

and

  2                                  

P = I  R        (P = I squared x R)

 

Let’s look at some examples of this: -

1) A lamp draws 1 amp of current at a voltage of 6 Volts. Joules’  Law combined with Ohms’ Law tells us that the lamp is burning 1 amp x 6 Volts = 6 Watts.

 

2) A DC circuit draws 2A of current, and has an overall resistance of 12 Ohms. Joules’ Law tells us that (2 x 2) amps of current x 12 Ohms = 48 Watts.

 

In Circuit

So that’s the very simple bit out of the way and dealt with. let’s now take a look at connecting resistances in parallel and also in series, as well as working out the total resistance: -

There are different equations for calculating parallel and series resistances. Let’s first take a look at series resistances:

In the example above we have a circuit diagram of 2 resistances, R1 and R2, in series. To calculate the total resistance of the series pair we simply add up the sum of the values of the two resistors thus: –

 

Rt = R1 + R2

 

That was easy.

When calculating the resistance of 2 resistors in parallel, however, things are slightly more complicated. The equation for calculating the total resistance of 2 resistors in parallel is:

 

Rt = (R1 x R2) / (R1 + R2)

 

Let’s look at an example of this: -

In the diagram above we have a 2,200 Ohm (2.2 kilohms) resistor connected in parallel with a 1,100 Ohm (1.1 kilohms) resistor. The total resistance is given by

 

Rt = (1,100 x 2,200) / (1,100 + 2,200)

Rt = 2,420,000 / 3300                            

Rt = 733.33 Ohms (0.73333 kilohms)

 

Lastly a reminder of the resistor colour code and how to read the resistance value of the component. (This code also applies to some capacitors too.) : –

 

 

 

 

Introducing Semiconductors

In this book I’m not going to be covering any other “passive” components, such as capacitors and inductors. – I’ll save that for book 2. Right now I’d like to move on to what are termed “active components”, or semiconductors.

All the many types of transistor are classed as semiconductors, as are a range of components called diodes. there are also semiconductor components called thyristors which are used for DC power control, also triacs which are used in AC power control circuitry. High-current versions of these are probably utilised in the power supply of your computer, along with capacitors – large and small, resistors, diodes, power transistors, and inductors. Here we are starting to go beyond the scope of this book, however.

Herein I’d rather stick, for now, with just resistors, diodes, and a single basic type of transistor known as a bipolar transistor.

 

 

Standard Transistor Symbol     Transistor Symbol Used Herein

 

 

Yes you have seen these symbols before. They appear in the Foreword.  I thought it prudent to place them here also to serve as a reminder of the point on circuit diagrammatic terminology touched upon therein, as well as to provide the circuit diagram symbol for a bipolar transistor. – No it’s not an electronic device with a mental condition. The name derives from its construction. See the link above for more information.

The bipolar transistor comes in 2 ‘flavours’; those being NPN and PNP:-

 

ollector                                                       mitter
NPN                                                                PNP

 

The meaning of these terms are described in detail in the Wikipedia article linked to above. This book isn’t written with an intention of dealing with the construction and function of electronic components. Foreknowledge in this area is assumed.. Links to locations which detail this are provided for those who need to know, however.

For the examples in this publication we’ll be using the NPN transistor.

 

Throughput

You will appreciate that every device has its limitations; therefore although there are expensive hi-current devices available that can handle several amps of power, most low-power, small signal bipolar transistors can only deal with a fraction of an amp passing through them without burning out. With this fact in mind we have to ensure that the current supplied to the individual transistor will not overload it. this is accomplished by a resistor connected between the collector and the + supply rail (VS). This resistor is commonly referred to as the “collector load resistor”. the amount of current allowed by this resistor is calculated by means of Ohms’ Law:

 

I=V/R

 

The main amount of current flowing through the device passes from collector to emitter. A smaller current is also required to be applied to the base connection, usually about 0.1 times or 10% (maximum) of the larger current.

 

Terminology

In electronics terminology we refer to the current flowing between collector and emitter as Ice0, and the current flowing between the diode junction of the emitter and base as Ieb0.

Similarly with respect to voltage, the terms Vce0 and Veb0 are used respectively.

The terms Vb, Vc, and Ve, refer to the voltage present at the transistor’s base, collector , and emitter respectively. Similarly the terms Ib, Ic, and Ie, refer to the current present likewise.

V+ usually refers to the supply voltage, otherwise referred to as VS or Vss.

 

Biasing the Base

A bipolar transistor requires a voltage of 0.7 volts present at its base before it will allow any current to pass between collector and emitter. This is known as the “transconductance threshold” It is for this reason, particularly where the device is used under small signal conditions such as audio amplification, that the base needs to be biased with a tiny current in proportion to the input signal, to a voltage of just under 0.7 volts.

To achieve this a pair of resistors connected in series across the supply rails is normally used as a potential divider. The resistances of each resistor are selected such that the voltage at the centre-tap to which the base is connected is just below 0.7 volts. In addition to this the resistances of the resistors are kept as high as is reasonably possible to ensure as little current as possible, and consequently as little wattage as possible, is wasted; as a potential divider will continue to burn the same amount of wattage whether or not an output is drawn from its centre point, due to it effectively being a resistance connected across the supply rails.

In the example above we use a 10 kilohm resistor as R1 and a 1.1 kilohm resistor as R2. The supply voltage, VS, is 7 volts.

To calculate the voltage at the centre tap between the two resistors, to which the transistor’s base is connected, therefore the base voltage (Vb), we use the following equation:

 

Vb = VS X (R2 / R1 + R2)

 

Therefore in this example: -

Vb = 7 X (1100 / (10000 + 1100))

Vb = 7 X (1100 / 11100)

Vb = 7 X (11 / 111)

Vb = 7 X 0.099099

Vb = 0.6693693V

 

- Which puts the transistor right at the edge of the threshold of transconductance. A voltage of over 31 millivolts will flip the device over into transconductance and a  proportionally equivalent current will flow between collector and emitter.

 

Beta

No this doesn’t refer to a test-version of a new computer program in this particular case: The beta of a transistor is the quantity giving the amplification factor of a transistor. There are two ways of looking at this; in-circuit and out-of-circuit.

Out-of-circuit, as a standalone unused component, a given type of transistor has a maximum beta rating that it can be run at in-circuit. This can vary from around 20 or less for some power-transistors, to up to 1500 or more for some hi-gain amplifier transistors.

Setting the beta of a transistor in-circuit is another part of circuit design.

The in-circuit beta of a given transistor can be calculated by the proportion of Ib  when Vb is above the transconductance threshold to the amount of current represented as Ice0. (Unless the transistor is connected in-circuit as a voltage amplifier rather than a current amplifier; in which case the beta is calculated by replacing the term Ib with Vb and Ice0 with Vce0. That is beyond the scope of this book, so we’ll stick to the current amplifier model for now.)

For example; let’s assume that we have a transistor connected in circuit with a base voltage of 0.75 volts (Vb = 0V75), therefore biasing it into transconductance. The base current is set at 1 milliamp (1mA). The supply voltage (VS) is 10 volts, and the collector load resistor is 100 ohms:

 

Ic (collector current) = V / R

Ic = 10 / 100

Ic = 0.1A (100mA)

 

The in-circuit beta of that transistor can then be given as:

 

b = Ic / Ib

b = 100 / 1

b = 100

 

Provided that this doesn’t exceed the transistor’s out-of-circuit beta rating it’s perfectly safe to run the transistor at this beta and expect its amplification factor to be 100 X.

(In most cases, though, such a large amplification factor in a single-transistor amplifier stage would give rise to signal distortion; especially in high-frequency AC amplifiers. For DC amplifiers such as we’re dealing with here, though, this beta rating is OK and won’t cause any distortion as there’s effectively nothing to distort in this example.)

 

 

 

Let’s sum up and take a look at an example of what we’re trying to achieve here:

In the circuit above we’re using the potential divider we mentioned earlier:

 

R1 = 10K and R2 = 1K1

 

That’s great with a supply voltage of 7V as it biases the base just below the transconductance threshold as we saw earlier.

- But we haven’t yet worked out Ib in this case. How do we do that? well the total current flowing in the potential divider will be:

 

VS / (R1 + R2)

 

7 / 11100 in other words; which equates to 0.00063A, or 63 microamps. That’s pretty low but it’s OK. If we want to run the transistor at a beta of 100 then we’ll need to make the collector load resistor allow 63 X 100 microamps to flow as Ice0.

So we want to arrive at a scenario where Ice0 = 6.3 mA.

We know just how to do that using Ohms’ Law:

If Ice0 = 6.3 mA and V=7 volts, then V / I = R:

 

7 / 0.0063 = 1111.1111 ohms

 

- Is the value of resistor that we’re looking for. we look in the spares box and find that the nearest value of resistor that we have is 1100 ohms (1K1). only 11.1111 ohms out; which will make very little difference except that the beta will be a fraction over 100. That’s good enough. – So we choose 1K1 as the value for the collector load resistor.

If we were to apply a current of 1mA at a gently rising voltage of anything above around 40mV to the base of the transistor then the collector voltage (Vc) would drop from 7 volts to near zero volts as the transistor starts to conduct.

Our circuit has caused the transistor to act as a voltage-triggered inverter: If a base voltage is present then there is no output from the collector-connected Vout 1. When no base voltage is present that same output is at rail voltage of 7v.

There are 2 “ends” of a transistor, however: The collector and the emitter: What would happen if we were to take the output from the emitter? (Vout 2) We should in theory get a different set of results – But before we’re able to do so we need to see to the matter of the emitter being connected directly to the negative rail; the most negative point of the circuit. We need an emitter resistor: -

What we did earlier was to select a 1K1 resistor as a collector resistor in order to prevent more than 6.3mA of current flowing through the transistor. If we share that and have a resistance equal to half of 1K1 (550 ohms) on both the collector and the emitter, then we still have an overall resistance of 1K1 in circuit and not more than 6.3mA of current flows; yet the transistor is now right in the middle of another potential divider.

Now, when there is no voltage at the base there is the full 7volts at the collector. When a voltage is introduced to the base the transistor conducts and the collector becomes the centre of the potential divider. Therefore Vc drops, but not to zero.:

In this case (Where Vt is the Vceo voltage of the conducting transistor.): -

 

Vt = VS X (R2 / R1 + R2)

Vt = 7 X (550 / 550 + 550)

Vt = 7 X (550 / 1100)

Vt = 7 X 1/2

Vt = 3 1/2 volts

 

So when a voltage is applied to the base the collector voltage Vc now falls from 7v to 3.5v. What of the emitter voltage Ve? When the transistor is not conducting there is no positive voltage present as such; therefore Ve = 0V. When the transistor fully conducts the emitter likewise becomes effectively the centre of the potential divider, and Ve rises to 3.5v.

So we have a situation where Vc = 3.5 to 7 V/Vsupply, and where Ve = 0 to 3.5V, depending upon the voltage potential of the transistor’s base at Vin.

Let’s stop designing here. We’ve designed a primitive single-transistor DC amplifier circuit; and we’ve covered the basics of Ohm’s Law etc as far as DC electrical resistance is concerned. We’ve also covered the function of a simple low-signal bipolar transistor: That’s quite an achievement in a short space of time.

I have touched on a few other electronic components, such as the diode, and I’ve not even gone there with a huge number of other components, such as the capacitor. Also I haven’t covered negative feedback either. Unfortunately that is beyond the scope of this book.

Nevertheless we covered a heck of a lot of material; and I’ve given you a basic idea of how Ohm’s Law is used in DC electronic circuit design. It is a bit condensed and heavy going, true, so read the entire book again in little bits, one point at a time.

 

I’ve managed to locate a copy of the original version of this crash course, and it is now available FREE as a pdf document by clicking this link.

* A pdf of the paperwork from the tutorials of a Basic Electronics Course is now available for FREE download on this site. (Download size = 5.55MB.)

To download it; click this link.