The rectifier circuit used in most electronic power supplies is the single-phase bridge rectifier with capacitive filtering, usually followed by a linear voltage regulator. The schematic for this rectifier is shown below in figure 1:

A large percentage of our transformers are used in rectifiers of the type illustrated in Figure 1, so we decided to dedicate this first edition of TRANSFORMER FACTS to rectifier transformers, and provide some practical tips for power supply designers.

"The AC current supplied to a rectifier always equals the DC current drawn from the rectifier when leakage currents in the diodes can be ignored."
Q: True or False?
A: True and False.

The opening statement is true if we compare average currents (I_m) on both the AC and the DC side of the rectifier. But AC current is always measured as RMS current (I_RMS), while DC current is always measured as average current (I_m). The opening statement is false if we compare I_RMS on the AC side with I_m on the DC side of the rectifier.

The RMS current (I_RMS) is always larger than the average current (I_m) because of the peaked shape of the AC current. When I_RMS is divided by I_m we obtain a measure of the peakedness of the current, which is called Form Factor. (F = I_RMS/I_m). The sharper the peaks are, the larger is the value of F.

The heating effect of an electrical current in wiring, resistors, and transformer windings is proportional to the square of the RMS current. The heating effect of the AC current in a rectifier circuit is accordingly proportional to I_S­² = (F x I_m)² = (F x I_L )², or the square of the DC current multiplied by F squared. The temperature rise in a given rectifier transformer is thus heavily dependent of the value of the Form Factor (F), and the required size of a rectifier transformer cannot be determined until the actual value of the Form Factor is known.

In a rectifier of the type shown in Figure 1, F has a value somewhere between 1.11 and 5.0 depending on the relative values of the impedances before and after the diode bridge. When these impedances are known, it is possible to calculate F (and U_C) using graphical methods published by Schrade¹ in 1943. But at that point the power supply designer usually has in his hand a prototype transformer, so U_C and I_S can be determined quickly by bench tests. (Be careful to measure I_S with a meter measuring true RMS current. Most AC current meters measure Im but are graduated in I_RMS, assuming F=1.11 which is only true for sinewave.

An accurate and simple method for determining the Form Factor (F) from oscilloscope readings with the aid of graphs developed by Toroid Corporation of Maryland is described below.

Let us assume we observe the current and voltage waveforms in different parts of the circuit of Figure 1 on a CRT oscilloscope, so we can compare waveforms before and after the diode bridge. Diagrams I-III show oscillograms for different values of the capacitor (C), assuming a transformer with negligible series inductance, such as a toroidal transformer.

The desired effect of the capacitor is to smooth the DC voltage, but at the same time it causes the AC current to flow in short bursts, which means higher F and larger RMS current in the transformer. The "conduction angle" (α) of the rectifier can be measured directly off the oscillogram - just remember that a full halfcycle is 180º.

It is clear that the Form Factor (F) must depend on the conduction angle (α). We have calculated the exact relationship between F and α for toroidal transformers, and the result is shown here in this graph. By measuring the conduction angle (α) off the oscilloscope a very accurate value for the Form Factor (F) can be read off the graph. Variations in DC load will change the conduction angle, and the corresponding changes in the Form Factor can easily be determined.

The graph sheet includes more information, which can serve as an aid to evaluating the trade-offs in power supply design. In the comments to the diagrams we have defined η=U_DC/ú_o, which relates the DC voltage to the peak no-load voltage of the transformer secondary. The flattening of the tops of the AC voltage waveform is caused by the voltage drop in the total impedance ahead of the diode bridge, so it is reasonable to assume that h must vary with the conduction angle (α). We have calculated this relationship also, again assuming toroidal transformers, and the result is shown in the graph sheet enclosed as a broken curve.

An important use of the graph for h is to determine the DC load regulation of a rectifier. DC load regulation δU_DC/U_DC = (1-η) x 100%. Remember that the diode voltage drops are included in the valued for U_DC. Each diode voltage drop can be assumed to be constant = 1V at all loads. The net load regulation is accordingly slightly worse than 1-η, especially for low DC voltages.

It is important to note that better efficiency of voltage conversion (as measured by η) can only be obtained at the cost of higher Form Factor, and conversely lower Form Factor can only be obtained at the cost of poorer DC load regulation.

The size of the transformer supplying the rectifier is proportional to the product of no-load voltage (U₀) and current capacity (I_S), which we call P_o. The dotted line in the graph sheet represents the lowest value of P_o required for any value of a (of any corresponding value of F or η) for a given DC power. (P_o/P_DC = F/η√2).

The transformer has a minimum size (P_o) of about 1.52 x P_DC (total DC power including diode losses) for a = 75º, where η= 0.8 and F = 1.7. Unfortunately it is not possible to stay near the minimum at all times, partly because better DC regulation than 20% is often required, and partly because the load-regulation of transformers varies widely with transformer size. DC load regulation and transformer load regulation are not proportional, but they generally increase and decrease together, so very small transformers tend to work at larger than optimal values of a, and very large transformers work at smaller than optimal values of α.

The design of a rectifier transformer to meet specific requirements for U_C, U_L, DC regulation, temperature rise, etc., requires exact data for both Form Factor (F) and rectification efficiency (η). But F and hare in turn determined by the data of the not-yet-designed transformer, so the power supply designer is caught in a "Catch-22" situation. One way out is to grab some old design, modify it some, and pray that the prototype will work.

Another way out is to let Toroid Corporation do the transformer design. Our application engineers have solid backgrounds in transformer and power supply design, and they have at their disposal interactive computer programs for transformer optimization, so they can design not only a transformer that will work, but also the most economical transformer that will do the job.

Diagram I

C=0. No regulator

Diagram II

C ’ Æ

Diagram III

C = normal (U_r /U_C<10%). Regulator working

O.H. Schrade: "Analysis of Rectifier Operation" Proceedings of the I.R.E., July 1943, pp.341-361. (This paper is difficult to find even in libraries. The important parts of the graphs are reprinted in MOTOROLA Silicon Rectifier Manual.)

Supply Voltages and Primary Windings for Power Transformers

The purpose of a power transformer is to convert AC supply voltage to one or more different AC voltages. In most cases it also provides electrical insulation between the supply voltage and the user's equipment.

The secondary windings of the transformer provide the voltages and currents required by the user to power lamps or motors, or to supply rectifiers. The Rated Power of the transformer is the sum of the VA (Volts x Amps) for all of the secondary windings.

The primary winding of a transformer must be designed to match the voltage and the frequency from the power source to the transformer, and must be able to transfer the necessary VA to the secondaries without overheating. The current carried by the primary winding thus depends on the secondary VA, but the voltage depends only on the power source.

Supply Voltages Worldwide

The power used by transformers in electronic equipment is single phase sinewave AC taken from a wall outlet, with the voltage and the frequency delivered by the local power utility.

The US Department of Commerce has published a booklet "Electric Current Abroad"ä which lists the voltages and frequencies used in each city around the world. Using this booklet as source, we have developed the following list of all single phase voltages and frequencies used and the number of countries where each voltage is used:

The allowable variation in voltage is normally ± 10% and the frequency is normally stable to better than .1%. The voltages and frequencies used in most industrialized countries are in bold. (Japan uses 100V 50Hz and 100V 60Hz.)

Some countries use different voltages and frequencies in different locations such countries are included in the country count more than once. To see the name of the country(countries) corresponding to each voltage, click here.

Nominal Primary Voltages

Ideally, the nominal primary voltage for a transformer should be equal to the nominal supply voltage, and the rated frequency should be equal to the supply frequency. It would obviously be impractical to follow these rules strictly and it is not necessary.

The transformer design does not impose any lower limit on the supply voltage. The output voltage from the transformer does, however, decrease with decreasing supply voltage, so a lower limit is set by the tolerance required for the secondary voltages. This tolerance is usually in the order of -10%

At the rated frequency, supply voltages higher than the nominal primary voltage will eventually cause noticeable mechanical hum or saturation effects, but a properly designed transformer should allow for more than + 10% headroom before this happens.

The transformer design does not impose any practical upper limit on how much the supply frequency can exceed the rated frequency, but a supply frequency lower than the rated frequency has the same effect as an overvoltage. The voltage headroom will be decreased by the percentage reduction in supply frequency below rated frequency, and a frequency larger than the rated frequency will increase the headroom. (A 50Hz transformer will have 6% headroom when run at 48Hz, but more than 32% headroom at 60Hz.)

As a general rule it can be assumed that it is safe to use a transformer for nominal supply voltages between about 95% and 105% of the transformer's nominal primary voltage. The listing below shows selected nominal primary voltages and corresponding ranges of supply voltages supported by each:

Multiple Primary Voltages

A transformer must be provided with more than one primary winding if it is to be used for several nominal voltages. One way to do this is to make a winding with several taps, but other methods are often more economical, as the following example will show:

A transformer for 115V primary voltage has a power rating of 210VA. The primary must supply 210VA to the secondary, plus the total losses in the transformer, say 20W. The primary current will thus be (210VA + 20W)/ 115V = 2.0A.

If we add turns to this primary so we get a second voltage of 230V, the primary current will be only (210 + 20)/230 = 1A when the total winding is used, but we cannot change the wire size in the 115V part of the primary. The second half of the primary will thus take up winding space when the 115V tap is used, but will not contribute to the output of the transformer.

If we instead make the transformer with two primary windings, each for 115V and 1A, we can connect the primaries in parallel for 115V supply, and in series for 230V supply. In both cases all the wire in the primary windings contributes to the output, so winding space is not wasted. As a result a smaller size transformer can be made.

A parallel/series connection works only when the high voltage is a whole multiple of the low voltage. Taps are needed for 100/120V or 220/240V, but the wasted winding space is quite small in these cases. If the primary must cover a wide range of voltages, it is always best to combine small taps with the series/parallel connection of the tapped windings.

Standard Primaries

At TOROID we use three types of primary windings as standard:

The color coding of these primaries is as shown.

A Quad primary has two blue leads and two red leads. Leads with like colors must be joined outside the transformer to form a blue and a red tap. This way of forming a tap is standard in all TOROID transformers.

The standard Quad primary is designed to have the two 100V windings in parallel for 100V operation, so a 6-lead voltage selector should be used. If the standard Quad primary is used with a 5-lead voltage selector, the rated VA for the transformer at the 100V tap must be reduced by about 4%. ( The 5-lead selector uses one half of the primary winding as an autotransformer for the 100V tap, so the primary copper losses are higher than for parallel 100V windings.)

Cores with primary windings of the three standard types are kept in inventory by TOROID for better economy and faster turnaround of small orders.

Upon request we will make primaries for any voltage or voltage combination, and with custom color coding.

How to Reduce Cost and Size of a Transformer

Correct specification of the secondary data is the most important rule for cost and size reduction of a transformer. Tips on how to specify secondary data for several transformer applications will be given in future issues of Transformer Facts.

The cost of a transformer increases with the size of the transformer and with the number of primary windings, so savings can also be made by following these rules for specifying primary data:

1. Do not specify a lower rated frequency than needed. (A 60Hz transformer has 20% higher rated power than a 50Hz transformer of the same size and weight.)
2. Do not specify more primary windings than needed. (Taps in the primary windings waste winding space, and thus make it necessary to make the transformer bigger.)
3. Do not specify more voltage headroom than needed. (The size of the transformer increases if the maximum supply voltage specified is larger than 110% of the nominal primary voltage.)

Conclusions:

Do not include extra safety margins. Tell us what you need, and let us decide what margins to allow.

You can save money by using a single-primary 60Hz transformer in USA and Canada, and using a 50Hz Dual primary or Quad primary only in other markets. We can design the two transformers to give identical output data, but your mechanical design must leave space for the larger 50Hz version.

Appendix to Section 1: Supply Voltages Worldwide - Used in at least one location in the country

There are several factors that make the toroidal transformer an advantageous choice compared to laminated transformers when impact on environment is a consideration:

1. A toroidal transformer weighs about half as much as a conventional transformer with the same capacity and heat rise. The main materials used in transformers are copper and steel, both of which are getting scarcer with cost increases as a consequence. We will explain how the weight savings can be explained in a separate newsletter.
2. No impregnation is needed to keep the laminates quiet so this potential environmental hazard is avoided.
3. The toroidal transformer fits into a smaller space, which allows chassis plates and enclosures to be smaller with less material used.
4. The lower weight reduces the cost and lessens the environmental impact of freight for raw material coming into our factory, transformers sent from us to you and outgoing freight for finished product from you to the end customer.
5. There is a much more efficient trade-off between size and temperature rise with a toroidal transformer when compared to a laminated transformer.

A toroidal transformer designed to run cooler will only be slightly larger than a “conventionally” designed transformer and will increase the overall efficiency of the equipment, lower demand for cooling in the equipment and increase the life span of other components in the equipment.

There are 2 factors that contribute:

1. In a laminated transformer core the individual E- and I-shaped laminates are stamped out of grain oriented steel. The magnetic flux travels easily along the grain but less well across the grain, which must be passed as part of the path around the bobbin. (See Fig 1)

   In a toroidal transformer, the core is wound like a roll of tape from grain oriented steel. The magnetic flux will go with the grain all the way around the core. (See Fig 2)

   As a consequence, a laminated transformer core can be used with a flux density of 10,000 to 12,000 Gauss (1.0-1.2 Tesla). A toroidal transformer core is normally calculated with a flux density of 15,000 to 16,000 Gauss (1.5-1.6 Tesla) which results in a weight reduction of about (1.2/1.5 x 100 =) 20%.

2. On a toroidal transformer core the copper wires are wound all around the circumference which allows for many turns before a new layer of the winding must begin.

   With a laminated transformer a bobbin is used to wind the primary and secondary windings. The width of the bobbin is limited as it must fit into the core (See Fig 3). As a result, many layers of windings must be wound and the length of the wire will increase with each layer and the average turn-length will be longer as more layers are needed. The weight of one turn of copper increases with the length of that turn so the total weight of copper for the whole winding will be higher than for a winding on a toroidal core where the (virtual) bobbin is much wider and fewer layers are needed with lower average weight per turn as a result (see Fig 4).

   A secondary, less important, effect also comes into play. With the longer average turn-length in the laminated transformer the resistance in the winding increases so either a heavier wire must be used or more turns are needed to compensate for the voltage drop in the winding.

   The actual weight savings for the toroidal winding compared to the laminated transformer winding is dependent on the actual design of a specific transformer but our experience over the years is that the toroidal transformer comes out at about 50% of the weight of a laminated transformer.

A current transformer is a type of transformer that is usually placed in the main circuit to step down a high current circuit to drive a low current device, usually a low current meter or resistor. It is also very useful in measuring or monitoring high current, high voltage and high power circuits. Current transformer (CT) applications can be found everywhere, such as:

1. In over-current or under-current protection circuits: The current transformer can drive an over-current relay as a switch, so when the main current exceeds the specification, the output voltage of the current transformer activates the relay and the protective circuit.
2. In high current monitoring circuit: A current transformer can step down the current for a low current meter to monitor the high current circuit. Or, a resistor can be connected in series with the current transformer output winding, when the stepped down current passing through this load resistor, results in a voltage over the resistor. This voltage can be used to monitor the high current circuit.
3. In high voltage current monitoring circuits: A current transformer can be used to step down the current, as well as used as an isolation transformer. It is a lot safer to use a current transformer to monitor the high voltage current circuit.
4. In remote circuit current status monitoring system: A current transformer can also be loaded with an LED as a discrete current indicator to monitor the circuit condition in a remote location. When the remote circuit current is flowing, the current transformer will generate enough current to light an LED to indicate the current flowing. When the remote current cease to flow, the LED will be turned off. This method can be used to indicate a stalled motor (unusual high current being generated) in a remote location.

There are two windings in a current transformer, one of them is a high current primary winding and the other is a low current secondary winding. Unlike in other transformers, the primary winding current in a current transformer is independent of the secondary winding load. The primary winding current depends only on the circuit into which the primary winding is connected. The primary winding is designed to have very low impedance (it often will only have one turn in the winding) and hence has negligible effect on the main current. Therefore, regardless of what change may be made to the secondary winding load, the primary winding current is always the same as that of the main circuit. One may argue that if the load on the secondary winding is changed, something in the primary winding has to change. This is partially true. The change is in the relationships between the several components of the primary winding current. The primary winding current is essentially made up of three components; the loss current that supplies iron and copper loss, the magnetizing current that establishes the flux in the core and the load current. However, these currents are not in phase with each other; there are differences in the phase angles and these angles change when the load changes. The primary winding current, as always, is the vector sum of these currents.

The design of the current transformer has to satisfy the equation: IinNin = IoutNout if the magnetizing and loss currents are not taken into account. If accuracy is a concern, then the magnetizing and loss currents must be kept small. The value Iin is determined by the circuit into which the primary winding is connected and Iout is by the load that is to be supplied. Iin verses Iout is the current ratio, which is the same as Nout verses Nin the turn ratio.

As mentioned earlier, the primary current consists of loss current, the secondary load and the magnetizing current. If high accuracy current transformer is needed, the loss and magnetizing current need to be kept as low as possible so that the secondary current will truly reflect the primary current which is also the current to be measured or sensed. As the result, a low-loss and high permeability core material shall be chosen.

The toroidal core is the most readily used core geometry for current transformer application. There is no air gap in the core so that the magnetizing current will always be small. Toroidal core geometry fits perfectly with flux flow in the core, therefore the core material can be utilized efficiently giving you a small core and small core loss as a result.

Caution: A current transformer should never be open-circuited while main current is passing through the primary winding. If the load is removed from the secondary winding while the main circuit current is flowing, most of the primary winding current becomes magnetizing current, but the vector angles change in such a way as to keep the total current in the primary the same as before. Because the main circuit is now mostly magnetizing current, the flux in the core shoots up to a high level and a very high voltage appears across the secondary. Due to the high turn ratio usually found in these transformers, the voltage in this condition can reach a dangerously high level, which can break down the insulation. It also becomes a hazard to personnel. The high flux can saturate the core and result in strong residual magnetism left in the core, thereby increasing magnetization current and introducing error in the transformation ratio. We strongly recommend that one put a short on the secondary winding before removing the secondary load while the main current is flowing through the primary winding.

A current transformer is a type of transformer that is usually placed in the main circuit to step down a high current circuit to drive a low current device, usually a low current meter or resistor. It is also very useful in measuring or monitoring high current, high voltage and high power circuits. Current transformer (CT) applications can be found everywhere, such as,

1. In over-current or under-current protection circuits: The current transformer can drive an over-current relay as a switch, so when the main current exceeds the specification, the output voltage of the current transformer activates the relay and the protective circuit.
2. In high current monitoring circuit: A current transformer can step down the current for a low current meter to monitor the high current circuit. Or, a resistor can be connected in series with the current transformer output winding, when the stepped down current passing through this load resistor, results in a voltage over the resistor. This voltage can be used to monitor the high current circuit.
3. In high voltage current monitoring circuits: A current transformer can be used to step down the current, as well as used as an isolation transformer. It is a lot safer to use a current transformer to monitor the high voltage current circuit.
4. In remote circuit current status monitoring system: A current transformer can also be loaded with an LED as a discrete current indicator to monitor the circuit condition in a remote location. When the remote circuit current is flowing, the current transformer will generate enough current to light an LED to indicate the current flowing. When the remote current cease to flow, the LED will be turned off. This method can be used to indicate a stalled motor (unusual high current being generated) in a remote location.

There are two windings in a current transformer, one of them is a high current primary winding and the other is a low current secondary winding. Unlike in other transformers, the primary winding current in a current transformer is independent of the secondary winding load. The primary winding current depends only on the circuit into which the primary winding is connected. The primary winding is designed to have very low impedance (it often will only have one turn in the winding) and hence has negligible effect on the main current. Therefore, regardless of what change may be made to the secondary winding load, the primary winding current is always the same as that of the main circuit. One may argue that if the load on the secondary winding is changed, something in the primary winding has to change. This is partially true. The change is in the relationships between the several components of the primary winding current. The primary winding current is essentially made up of three components; the loss current that supplies iron and copper loss, the magnetizing current that establishes the flux in the core and the load current. However, these currents are not in phase with each other; there are differences in the phase angles and these angles change when the load changes. The primary winding current, as always, is the vector sum of these currents.

The design of the current transformer has to satisfy the equation: IinNin = IoutNout if the magnetizing and loss currents are not taken into account. If accuracy is a concern, then, the magnetizing and loss currents must be kept small. The value Iin is determined by the circuit into which the primary winding is connected and Iout is by the load that is to be supplied. Iin verses Iout is the current ratio, which is the same as Nout verses Nin the turn ratio.

As mentioned earlier, the primary current consists of loss current, the secondary load and the magnetizing current. If high accuracy current transformer is needed, the loss and magnetizing current need to be kept as low as possible so that the secondary current will truly reflect the primary current which is also the current to be measured or sensed. As the result, a low-loss and high permeability core material shall be chosen.

The toroidal core is the most readily used core geometry for current transformer application. There is no air gap in the core so that the magnetizing current will always be small. Toroidal core geometry fits perfectly with flux flow in the core, therefore the core material can be utilized efficiently giving you a small core and small core loss as a result.

Caution:

A current transformer should never be open-circuited while main current is passing through the primary winding. If the load is removed from the secondary winding while the main circuit current is flowing, most of the primary winding current becomes magnetizing current, but the vector angles change in such a way as to keep the total current in the primary the same as before. Because the main circuit is now mostly magnetizing current, the flux in the core shoots up to a high level and a very high voltage appears across the secondary. Due to the high turn ratio usually found in these transformers, the voltage in this condition can reach a dangerously high level, which can break down the insulation. It also becomes a hazard to personnel. The high flux can saturate the core and result in strong residual magnetism left in the core, thereby increasing magnetization current and introducing error in the transformation ratio. We strongly recommend that one put a short on the secondary winding before removing the secondary load while the main current is flowing through the primary winding.

Medical Grade Transformers generally refer to the transformers used in medical devices as well as hospital, biomedical and patient care equipment. There are a number of strict safety rules, guidelines and laws governing the design, construction and the test of these transformers. These safety rules, guidelines and laws include, but are not limited to:

• The limit of maximum earth leakage current
• The maximum patient leakage current
• The maximum enclosure leakage current
• The maximum patient auxiliary current
• The values of test voltage (high potential voltage test between windings)
• The minimum creepage distance
• The minimum air clearance
• The maximum temperature rise at load and at over load

One can find these rules and regulations in UL 2601-1, IEC 601-1, CSA C22.2 No. 601 and EN 60601-1 standards.

The majority of medical grade transformers are isolation transformers.

There are generally two types of isolation, one that relies on Safety Ground (Protective Earth), and one that relies on Double or Reinforced Insulation. A transformer that relies on safety ground uses a basic isolation between the primary and the safety shield and shield to secondary. This shield has to be thick to be able to meet required tests in the safety standard. If the isolation breaks, the electrical path goes directly to ground, providing safety. For a transformer that relies on double or reinforced Insulation there is no "safety" shield, but the insulation as indicated by the name, is much thicker. It is designed so that all layers of the insulation can pass the thickness and high potential voltage tests required by the standard. If one insulation layer breaks, the next layer will be able to provide the required safety. In both the design options, the construction design must still meet the required creepage and clearance requirements. If the transformer includes a static shield for noise reduction, it is important to note that this shield does not provide the transformer with Safety Ground but it working as a functional earth. When the shield is grounded, it attenuates the common mode noise and can reduce the leakage current from the primary to the secondary winding (please note that this leakage reduction is not the same as when measured Primary to Ground).

Normally, without extra mechanical barriers between the primary and shield and secondary, a transformer with double/reinforced insulation has lower leakage current than the one with Safety Shield.

A Safety Shield wire should be connected to the Protective Earth terminal in the equipment while the Static Shield, if included, should be connected to the Functional Earth terminal.

We have found that most design engineers are not aware of the subtle nuances they receive with their toroidal transformer. By soldering on a (heavy) insulated wire to a secondary and adding turns on top of the Mylar Insulation, you can increase the voltage of the prototype. Conversely, you can decrease the voltage of the transformer by reversing the direction of the turns. This allows you to perform very simple fine-tuning of your prototype without having to order a completely new one.

Step 1: Determine which winding you want to adjust the output voltage on.
Step 2: Splice/Solder on additional wire to one of the leads of that winding.
Step 3: Put the lead(s) through the center hole and bring it back to the original point. If the direction of the winding is in the same direction of original winding, it adds one turn on the transformer. If the winding direction is opposite to the direction of original winding, you subtract one turn. To add on or take off more turns, just repeat the process more times.
Step 4: It is important to measure the voltage after the first turn so you can see how much voltage you are adding or subtracting from your lead. Measuring your voltage after the first turn will also give you a better idea of exactly how many turns you will need to reach your desired voltage.

Here are some guidelines for how many turns you may need for 60Hz transformers: