In this tutorial about transformers I will explain the basics in simple terms. As we know transformers can work without any moving parts inside and it is mainly used to change voltage levels so that we can transfer energy from one circuit to another through electromagnetic induction.
We use alternating current (AC) in our homes and workplaces because it is easy to generate AC at the suitable voltage levels. Using a transformer (which is why it’s called a “transformer”), we can increase this voltage to much higher levels. This high-voltage electricity is then sent across long distances through the national grid, using pylons and cables.
The reason we increase the voltage is that higher voltage means lower current for the same power. Lower current reduces heat losses (known as I2R losses) in the cables.
Once this high-voltage electricity reaches its destination then transformers reduce it to lower, safer levels for use in homes and workplaces. All of this becomes so easy simply because of how voltage transformers work to change voltage levels efficiently.
The Voltage Transformer
The Voltage Transformer is a straightforward electromagnetic device. It doesn’t move around or do anything, instead it sits there quietly, doing its job based on the principles laid out by Faraday’s law of induction.
This law is all about how electrical energy can be transformed from one level to another which is exactly what the transformer does.
Now how does it work? It works by connecting several electrical circuits through a common oscillating magnetic circuit that it creates. The actual operation of transformers really hinges on something called “electromagnetic induction,” specifically through a process known as Mutual Induction.
So what’s Mutual Induction all about? When you have one coil of wire sitting close to another coil, the first coil can actually induce a voltage in the second coil just by using magnetic forces. Because of this mutual interaction, we can say that transformers operate within what we like to call the “magnetic domain.”
And the name “transformer” comes from its incredible ability to “transform” voltage or current levels from coil to another.
How Transformers are able to Transform Electrical Power
These handy gadgets can either increase or decrease the voltage and current levels of the electricity they are managing. And what is even better? They achieve this without manipulating the frequency or altering the overall electrical power transferred between windings via the magnetic circuit. Isn’t it quite impressive?
Upon closer inspection of a single-phase voltage transformer it becomes evident that it consists of two wire coils. We have one coil named the “Primary Winding” and another coil known as the “Secondary Winding.”
In this brief tutorial let jus consider the “primary” side as the usual recipient of power and the “secondary” side as the location where the power is distributed. To clarify, in a voltage transformer with a single phase, the primary side usually has the higher voltage.
This is where it becomes intriguing, these two coils are not physically connected electrically. Instead they are bundled around the central closed magnetic iron circuit called the “core.” The core is not simply a single block of iron, it consists of separate laminations that are joined.
This smart design helps minimize magnetic losses that may happen in the core. Therefore as we consider transformers, we can admire how they adeptly handle power without establishing direct electrical connections between their coils!
Even though these two windings (primary and secondary) are electrically isolated from each other, meaning they don’t have any direct electrical connection, they’re actually magnetically linked through that common core we talked about earlier.
This clever setup allows electrical power to be transferred from one coil to the other without any wires connecting them!
Now when we have an electric current flowing through the primary winding, it creates a magnetic field around it. This magnetic field is super important because it induces a voltage in the secondary winding.
So in a nutshell when we send current through the primary, it sets off a chain reaction that allows power to flow into the secondary winding. This whole process is at the heart of how transformers operate as depicted below:
Understanding the Single Phase Voltage Transformer
In simple terms, it is important to remember that there is no direct electrical connection between the two coil windings in a transformer. This distinct characteristic is what gives it the nickname of an Isolation Transformer. Isn’t that awesome.
Lets now explore the mechanics behind all of this. Usually we observe that the main coil of a transformer is connected to the incoming voltage source. Here the incoming electrical power is converted into a magnetic field which is a very interesting process.
Next there is the secondary coil with its own crucial role to play. The purpose of it is to transform the alternating magnetic field generated by the primary coil back into electrical energy. As depicted in the illustration, this procedure generates the necessary output voltage.
Hence, there is an incredible collaboration taking place between the primary and secondary coils, eventhough there is no direct electrical link. We can learn more about this in the following section:
How a Single-phase Transformer is Constructed
Where:
- VP represents the Primary Voltage
- VS indicates the Secondary Voltage
- NP denotes the Number of Primary Windings
- NS depicts the Number of Secondary Windings
- Φ (phi) shows the Flux Linking the Windings
So these two coil windings in a transformer, they are not electrically connected to each other at all. Instead they’re linked magnetically. This is a key feature of how transformers work.
The Basics of Transformer Operation
Now a single-phase transformer has the ability to either increase or decrease the voltage that’s applied to its primary winding. This flexibility is what makes transformers so useful in various applications.
- Step-Up Transformers: When a transformer is used specifically to “increase” the voltage on its secondary winding compared to whats applied to the primary, we call it a Step-up transformer. This means that the output voltage is higher than the input voltage which can be really handy in certain situations.
- Step-Down Transformers: On the contrary when a transformer is used to “decrease” the voltage on its secondary winding relative to the primary, we refer to it as a Step-down transformer. In this case the output voltage is lower than what we put into the primary winding.
The Impedance Transformer
But there’s actually a third condition that we should be aware of. In this scenario a transformer produces the same voltage on its secondary winding as what’s applied to its primary winding.
In other words the output voltage is exactly same as the input voltage, along with matching current and power transfer.
This type of transformer is known as an “Impedance Transformer.”
It is primarily used for impedance matching or for isolating adjacent electrical circuits from each other.
How Voltage Differences Are Achieved
Now you might be wondering how we achieve that difference in voltage between the primary and secondary windings.
Well, it all comes down to changing the number of coil turns in the primary winding (which we denote as NP) compared to the number of coil turns in the secondary winding (denoted as NS). By adjusting these turns we can control whether we’re stepping up or stepping down the voltage.
Understanding the Turns Ratio in Transformers
So since a transformer is fundamentally a linear device, there’s a specific ratio that comes into play between the number of turns of wire in the primary coil and the number of turns in the secondary coil.
This ratio is what we call the “turns ratio” or more formally, the ratio of transformation (TR).
This turns ratio is super important because it essentially dictates how our transformer operates and determines the voltage that we can expect to see on the secondary winding.
Why the Turns Ratio Matters
It is really crucial for us to know how many turns of wire are on the primary winding compared to those on the secondary winding. The turns ratio itself doesn’t have any units, it simply compares these two windings in a straightforward way.
We usually express this ratio using a colon, like 3:1 (which we say as “three to one”).
Example of Turns Ratio
Let us now clarify this with an example. If we have a turns ratio of 3:1 that means if there are 3 volts present on the primary winding then we will get 1 volt on the secondary winding.
So it’s a straightforward relationship: 3 volts on the primary translates to 1 volt on the secondary.
This also means that if we change the number of turns in either winding then the resulting voltages will also change according to that same ratio.
The Importance of Ratios in Transformers
Transformers are all about these “ratios.” We are looking at the ratio of primary to secondary, the input to output ratios and of course the turns ratio will always match up with its corresponding voltage ratio.
In simpler terms for any given transformer we can say that “turns ratio = voltage ratio”.
What’s really interesting is that when it comes to transformers, the actual number of turns on any winding is not what matters the most, it is really all about that turns ratio, as indicated in the following formula:
Transformers Turns Ratio Formula
NP/NS = VP/VS = n = Turns Ratio
So let’s assume we are working with an ideal transformer and we’re looking at the phase angles where ΦP (the phase angle of the primary) is equal to ΦS (the phase angle of the secondary).
Now when we express a transformer’s turns ratio, the order of those numbers really matters.
For example if we say the turns ratio is 3:1 that indicates a very specific relationship between the primary and secondary windings. This means that for every three turns on the primary winding there is one turn on the secondary winding.
On the contrary side if we were to express the same relationship as 1:3, it completely changes everything! In this case we’re saying that for every single turn on the primary winding, there are three turns on the secondary. This distinction results in a very different output voltage and transformer behavior.
Solving a Transformer Turns Ratio Problem #1
We have got a transformer that has 1800 turns of wire wrapped around its primary coil and 600 turns of wire on its secondary coil. Now we need to find out what will be the turns ratio (TR) of this transformer?
To calculate this we simply take the number of turns in the primary coil and divide it by the number of turns in the secondary coil.
So in our example we would calculate it like this:
Turns Ratio (TR) = Number of Turns in Primary Coil / Number of Turns in Secondary Coil
T.R. = NP/NS
Then substituting in our numbers, that gives us:
TR = 1800 turns (primary) / 600 turns (secondary) = 3:1
When we do the math we find that the turns ratio is 3:1. This tells us that for every three turns on the primary coil there is one turn on the secondary coil.
Solving a Transformer Voltage Calculation Problem #2
Now if we proceed to apply 220 volts RMS to the primary coil of the transformer we discussed above, we are interested in determining what the secondary no-load voltage would ultimately be??
T.R. = 3:1 or 3/1 = VP/VS = Primary Volts/Secondary Volts = 220/VS
∴ Secondary Volts, VS = VP/3 = 220/3 = 73.33 Volts
Just to clarify again, here we are dealing with a “step-down” transformer since the primary voltage is set at 220 volts, and the secondary voltage is lower, coming in at 80 volts.
Now the main thing we need to remember about transformers is that their job is to change voltages based on specific ratios. We can see that the primary winding has a certain number of windings which are basically coils of wire, designed to match that input voltage we mentioned.
If we want the secondary output voltage to be exactly the same as what’s coming into the primary winding then we need to have the same number of coil turns on the secondary core as there are on the primary core.
This creates a nice even turns ratio of 1:1 (or 1-to-1) meaning for every one coil turn on the secondary, there is one coil turn on the primary.
On the flip side if we want the output secondary voltage to be higher than what we are putting in (which makes it a step-up transformer) then we need to have more turns on the secondary winding.
This would give us a turns ratio of 1:N (1-to-N) where N is that turns ratio number.
Similarly if we are looking to have the secondary voltage be lower than what’s coming from the primary (like in our step-down transformer scenario) then we need fewer windings on the secondary side, resulting in a turns ratio of N:1 (N-to-1).
Real Life Working of a Transformer
we’ve talked about how the number of coil turns on the secondary winding when compared to the primary winding, really influences the voltage we get from that secondary coil.
But the question is if those two windings are electrically isolated from each other how exactly do we get that secondary voltage?
Well let’s remember what we said before, a transformer is basically made up of two coils that are wound around a shared soft iron core.
When we apply an alternating voltage (let’s call it VP) to the primary coil, current starts flowing through it.
This flow of current creates a magnetic field around the coil. This whole phenomenon is what we refer to as mutual inductance and it’s all based on Faraday’s Law of electromagnetic induction.
As the current increases from zero up to its maximum value the strength of that magnetic field builds up too. This change in magnetic flux is represented as dΦ/dt.
As the magnetic lines of force created by this electromagnet spreads out from the coil, the soft iron core acts like a highway, guiding and concentrating that magnetic flux.
This magnetic flux links the turns of both windings, increasing and decreasing in opposite directions as it responds to the alternating current (AC) supply.
Now the strength of the magnetic field that gets induced into that soft iron core really depends on two main things, the amount of current flowing through and the number of turns in the winding. So when we reduce the current, we also see a decrease in the strength of that magnetic field.
When those magnetic lines of flux travel around the core, they pass through the turns of the secondary winding.
This movement causes a voltage to be induced in the secondary coil. The amount of voltage we get is determined by Faraday’s Law which tells us that it’s equal to N times dΦ/dt, where N is the number of coil turns.
Plus, it’s worth noting that this induced voltage has the same frequency as what we see in the primary winding voltage.
What this means is that each turn of wire in both windings experiences the same voltage because they’re all linked by that same magnetic flux.
So if we look at it closely, the total induced voltage in each winding is directly proportional to how many turns are in that winding. However if there are significant magnetic losses in the core then we might find that the peak amplitude of the output voltage available on the secondary winding gets reduced.
If we want to boost that primary coil’s ability to generate a stronger magnetic field, enough to counteract those core losses, then we have a couple of options. We can either increase the current flowing through the coil or keep that current steady and instead boost the number of turns in the primary winding (let’s call it NP).
The combination of amperes and turns is known as “ampere-turns” and it essentially defines how strong our magnetizing force is.
Now let’s imagine we have a transformer with just one turn in both the primary and secondary coils. If we apply one volt to that single turn in the primary coil, assuming there are no losses then enough current will flow and enough magnetic flux will be generated to induce one volt in that single turn of the secondary coil as well.
In other words, each winding supports an equal number of volts per turn.
As this magnetic flux varies sinusoidally, represented by Φ = Φmax sinωt, we can establish a basic relationship for induced electromotive force (emf) denoted as E, in a coil with N turns. This relationship can be summed up through the following equation:
emf = turns * rate of change
E = N(dΦ/dt)
E = N * ω * Φmax * cos(ωt)
Emax = N * ω * Φmax
Erms = (Nω/√2) * Φmax
= (2π/√2) * f * N * Φmax
∴ Erms = 4.44fNΦmax
- In the above formula:
- f represents the flux frequency in Hertz = ω/2π
- Ν indicates the number of coil windings.
- Φ denotes the amount of flux in webers
Understanding the Transformer EMF Equation
So the Transformer EMF Equation is what we are discussing here. N is the number of primary turns which we indicate as (NP) when we examine the primary winding emf. Conversely when we talk about the secondary winding emf N will stand for the quantity of secondary turns, or NS.
It’s crucial that we remember that transformers require an alternating magnetic flux in order to function correctly.
This implies that transformers are completely incapable of converting or supplying DC voltages or currents.
The explanation for this is rather simple: transformers simply cannot function with steady state DC voltages because a fluctuating magnetic field is required to create a voltage in the secondary winding.
Only pulsing or alternating voltages are compatible with them.
Assume for a minute that the primary winding of a transformer is connected straight to a DC source.
Since DC has no frequency the winding’s inductive reactance would be 0 in such scenario.
As a result the winding’s effective impedance drops to a level that is essentially equivalent to the resistance of the copper wire that is employed in it.
This winding would therefore pull an abnormally high current from the DC supply.
It would overheat and finally burn out due to this high current. Furthermore as we all know from elementary physics I is equal to V divided by R.
Solving a Transformer Problem to Calculate its Main Parameter, Problem #3
Let us consider the primary winding of a single-phase transformer. This primary winding has a total of 500 turns. Next the secondary winding has 100 turns. This difference in the number of turns between the primary and secondary windings is really important for how the transformer operates.
Now when we apply a voltage of 2300 volts to the primary winding of the transformer while it is running at a frequency of 50 Hz the magnetic flux density within the transformer reaches its maximum value which is measured at 1.1 Tesla. Let us calculate the following parameters:
1) Calculate the maximum flux in the core:
Erms = (Nω/√2) * Φmax
Φmax = Erms/Nω * √2 = (2300/(500 * 2π * 50)) * √2
∴ Φmax = 0.0207 Wb or 20.7mWb
2) Calculate the cross-sectional area of the core:
Φmax = β * A
∴ A = Φmax/β = 0.0207/1.1 = 0.018 m2
3) Calculate the EMF induced in the secondary winding:
ES(rms) = 4.44 * f * N * Φmax
ES(rms) = 4.44 * 50 * 100 * 20.7 * 10-3
∴ ES(rms) = 459.54 Volts
Given that the the secondary induced emf and the secondary voltage rating are equivalent, the secondary voltage may also be calculated more easily using the turns ratio as follows:
T.R. = VP/VS = NP/NS
∴ VS = (VP * NS)/NP = (2300 * 100)/500 = 460 Volts
Understanding the Power Rating of a Transformer
Another really important thing we need to know about transformers is their power rating. The power rating of a transformer is figured out by taking the current and multiplying it by the voltage. This gives us a rating in Volt-amperes which we often write as VA.
Now when we talk about smaller single-phase transformers we can just rate them in volt-amperes. But when we get to much larger power transformers things change a bit.
These bigger transformers are rated in Kilo volt-amperes which we write as kVA. To give you an idea 1 kilo volt-ampere is equal to 1,000 volt-amperes. And if we go even bigger we have Mega volt-amperes which we write as MVA where 1 mega volt-ampere is equal to 1 million volt-amperes.
In a real life transformer where we do not consider any losses, the power in the secondary winding is going to be equal to the power in the primary winding.
This means that these transformers are constant wattage devices which means they change the voltage to current ratio but do not change the power itself.
Because of this in a perfect transformer the Power Ratio equals one which we also call unity since the product of voltage which we write as V and current which we write as I stays constant.
Now here is how it works: the electric power at a certain voltage and current level on the primary side gets “converted” into electric power at the same frequency and at the same voltage and current level on the secondary side.
Although we can use transformers to increase or decrease voltage they cannot actually increase power.
So when a transformer increases voltage it ends up decreasing current and when it decreases voltage it increases current.
This way the output power always stays equal to the input power. Therefore we can confidently say that primary power is equal to secondary power which we can write as (PP = PS).
Formula for Calculating Transformer Power
PowerPrimary = PowerSecondary
P(PRI) = P(SEC) = VP * IP * cosΦP = VS * IS * cosΦS
In this formula we have ΦP which represents the primary phase angle and then we have ΦS which represents the secondary phase angle.
Now let us keep in mind that power loss is connected to the square of the current. We can write this as I²R.
So if we decide to increase the voltage let us say by doubling it which we can write as ×2 the current would decrease accordingly which means it would drop to half or ÷2.
Even with this change we would still be providing the same power to the load. This results in a reduction of losses by a factor of 4 which is pretty significant.
Now if we raise the voltage by a factor of 10 the current would also drop by that same factor which means it would go down to one-tenth.
This leads to an overall reduction of losses by a factor of 100. So it is clear that adjusting voltage can really make a difference in reducing power losses.
Understanding Transformer Efficiency
Transformers work without needing any moving parts to pass energy from one place to another. What this really means is that we do not have to worry about losing energy due to things like friction or wind resistance which can be a real problem with other electrical gadgets.
However it is important to note that transformers are not completely free from losses. They do experience some other types of losses that we call “copper losses” and “iron losses.” But honestly these losses are usually pretty small compared to what we might see elsewhere.
Copper Losses
Now when we talk about copper losses we are referring to something known as I²R loss. This is basically the electrical power that gets wasted as heat because of the currents flowing through the copper windings inside the transformer. That is where the name comes from!
Copper losses tend to be the biggest culprit when it comes to energy loss during a transformer’s operation. If we want to figure out how much power is actually lost (for each winding) we can do a little math.
We take the amperes square that number and then multiply it by the winding’s resistance measured in ohms (I²R). It sounds a bit technical but it is pretty straightforward.
Exploring Iron Losses
Now let us talk about iron losses which are also known as hysteresis losses. These happen when the magnetic molecules in the core of the transformer do not quite keep up with the alternating magnetic flux. Essentially they lag behind a bit.
This lagging happens because it takes some energy to flip those magnetic molecules around, they will only change direction once the magnetic flux has built up enough strength to make them do so.
Understanding Energy Loss in Transformers
Now let us learn about energy loss in transformers. When the magnetic molecules in the core of the transformer reverse their direction it creates friction and this friction generates heat in the core.
This heat is actually a type of energy loss that we need to be aware of. Now one way we can reduce this hysteresis loss in transformers is by making the core from certain special steel alloys that are designed to minimize this effect.
The Effect of Power Loss on Efficiency
Now the amount of power loss in a transformer really affects how efficient it is overall.
We can think of the effectiveness of a transformer as being shown by the power or wattage loss that occurs between the primary side where we input energy and the secondary side where we get our output.
Because of this we can say that the efficiency of a transformer is determined by looking at the ratio of the power output from the secondary winding which we call PS to the power input into the primary winding which we call PP.
This ratio gives us a good idea of how efficient the transformer is and it tends to be quite high.
The Ideal vs. Actual Efficiency
Now if we imagine an ideal transformer it would operate at 100% efficiency meaning it would transfer all electrical energy from its primary side to its secondary side without losing any along the way.
But in reality actual transformers are not completely efficient. When they are working at full load capacity their peak efficiency usually comes somewhere around 94% to 96% which is still impressive for any electrical device if you ask me.
For any transformer that is running at a stable AC voltage and frequency it can sometimes achieve an efficiency as big as 98%. Efficiency in terms of transformers, we often use the symbol η to define it as follows:
Formula for Calculating Efficiency in transformers
Efficiency, η = (Output Power/Input Power) * 100%
= (Input Power – Losses)/Input Power * 100%
= (1 – (Losses/Input Power)) * 100%
Where Power is the unit of measurement for input, output, and losses.
The main watts in transformers are typically referred to as “volt-amps,” or VA, to distinguish them from the secondary watts. The above efficiency equation can thus be further simplified to:
Efficiency, η = Secondary Watts (Output) / Primary VA (Input)
When studying the fundamentals of transformers it can occasionally be simpler to recall the connection between the input, output, and efficiency of the transformers when employing visual aids.
A triangle with power in watts at the top, volt-amps at the bottom and efficiency at the bottom is created by superimposing the three values of VA, W, and η. The exact placement of each quantity in the efficiency formulae is represented by this arrangement.
Efficiency Triangle for Transformers
and the following permutations of the same equation are obtained by incorporating the triangle quantities mentioned above:
So now you can easily find power using the formula, Watts (output) = VA x eff, or you can find VA (input) using the formula VA= W/eff, or to find Efficiency you can use the formula eff. = W/VA, etc.
Conclusions
So to sum it all up this tutorial has given us a good overview of the basics of transformers.
A transformer is a device that changes the voltage or current coming into its input winding into a different value that comes out of its output winding and it does this by using a magnetic field.
At its core a transformer is made up of two coils that are electrically separated and it operates based on Faraday’s principle of mutual induction.
This means that an electromotive force or EMF is generated in the transformer’s secondary coil thanks to the magnetic flux that is created by the voltages and currents flowing through the primary coil winding.
How Transformers Are Built
Now if we take a closer look at how these windings are set up we see that both the primary and secondary coils are wrapped around a shared soft iron core.
This core is made from different laminations which helps to reduce those pesky eddy currents and power losses that can occur.
The primary winding is connected to an AC power source and it is important for that power to be sinusoidal. Meanwhile the secondary winding is what provides electrical energy to whatever load we are using.
Reverse Functionality
That being said we should also know that a transformer can actually work in reverse too.
If we connect the supply to the secondary winding it can still function as long as we pay attention to the voltage and current specifications that need to be followed.
Understanding Transformer Types
Talking about how the primary and secondary windings of a transformer work together. This relationship can lead us to have either a step-up voltage transformer or a step-down voltage transformer.
We describe this relationship through the turns ratio or transformer ratio which is basically the ratio of the number of turns in the primary winding to the number of turns in the secondary winding.
Step-Up and Step-Down Transformers
Now if this turns ratio is lower than one which we can write as n < 1 it means that the number of turns in the secondary winding NS is greater than the number of turns in the primary winding NP.
This situation classifies our transformer as a step-up transformer because it increases the voltage.
On the contrary if this ratio is greater than one which we can express as n > 1 it indicates that NP is greater than NS. In this case we categorize our transformer as a step-down transformer because it reduces the voltage.
Flexibility of Transformers
It is also really important for us to note that a single phase step-down transformer can actually work as a step-up transformer too.
All we need to do is reverse its connections and designate the low voltage winding as the primary winding and switch things around for the secondary winding.
Of course we have to make sure that the transformer operates within its original VA design rating to keep everything safe and sound.
Exploring the Turns Ratio in Transformers
So what happens when the turns ratio is one or unity which we can write as n = 1.
This means that the primary and secondary windings have the exact same number of coil turns.
Because of this equality we can expect that the voltages and currents will be identical across both windings which is pretty neat.
The 1:1 Transformer
Now this type of transformer that has a 1:1 turns ratio is known as an isolation transformer.
The reason we call it that is because both the primary and secondary windings have an equal number of volts per turn which helps to keep things balanced.
When we talk about the efficiency of a transformer we are really looking at how much power it supplies to the load compared to the power it takes from the source.
In an ideal or perfect transformer there are absolutely no losses at all which means there is no power loss so we can say that PIN equals POUT.
References:
How can you use a transformer with an AC current?