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Circuit Surgery Regular clinic by Ian Bell Transformers and LTspice – Part 1 T his month, we will look at the basics of transformers and some aspects of simulating transformer circuits in LTspice. A transformer is a passive electronic device that transfers electrical energy, in the form of alternating current, from one circuit to another without using an electrically conductive connection. A transformer comprises two or more coils (looped conductors) in close physical proximity, one of which is used for the energy/signal input (called the primary winding). This coil creates an alternating magnetic field which, by virtual of their closeness, passes through the other coil(s) (the secondary winding(s)), producing a voltage across these windings, which will cause current to flow if they are connected to a load. Transformers come in a very wide range of formats, from tiny surfacemount RF devices to the huge (size of a house) power transformers used in national electrical distribution networks. In between are the transformers used in linear and switched-mode power supplies, pulse transformers used in communications, audio transformers and many other specialist types. The key properties of transformers are that they provide electrical isolation between Mag netic f lux C hang ing current Ind uced vo ltag e P rimary Second ary Fig.1. Basic transformer: two coils linked by magnetic flux. Simulation files Most, but not every month, LTSpice is used to support descriptions and analysis in Circuit Surgery. The examples and files are available for download from the PE website. 58 circuits, they can change voltage levels and they change they effective impedance of a load connected via a transformer rather than directly. Electromagnetic induction Electric current (DC or AC) creates a magnetic field around a wire. If the wire is wound in a loop the field in the centre of the loop is more concentrated. The fundamental physics of the transformer is called ‘electromagnetic induction’ and was discovered by Michael Faraday and Joseph Henry in the 1830s (for which they were honoured by having important SI units named after them – the farad and henry). Electromagnetic induction is the creation of electromotive force (‘emf’, measured in volts) across an electrical conductor by a changing magnetic field. In a transformer, a changing current in one conductor creates a changing magnetic field which induces an emf in another conductor. A changing magnetic field is required for electromagnetic induction, so although a steady (DC) current creates a magnetic field, AC is required for transformer operation. Electromotive force Electromotive force is not a mechanical force – it is the electrical action produced by a non-electrical energy source (eg, chemical energy from a battery or the electromagnetic induction in a transformer). It drives current to flow in a conducting circuit or produces voltage across an open circuit due to the separation of charge. For an open circuit, the charge separation creates an electric field which opposes the separation of charge in balance with the emf driving the separation. The open-circuit voltage is equal to the emf. Transformer action Fig.1 shows two coils in close proximity. Applying a varying current to one coil will create the magnetic field, which is visualised as magnetic flux lines. Some of the magnetic flux will pass through the second coil, resulting in an induced emf (and hence voltage across the coil). Not nearly all of this flux passes through the second coil so this arrangement will Mag netic f lux C ore P hasi ng d ot C hang ing current + + – – P rimary: N 1 turns Second ary: N Ind uced vo ltag e 2 turns Fig.2. Transformer with core – this is much more efficient than the transformer in Fig.1. produce a poor transformer – it will not be efficient in transferring energy from the secondary to the primary. The situation can be improved by using a transformer core, as shown in Fig.2. If the core material and structure is carefully chosen (particularly its magnetic properties), then the majority of the flux will be contained in the core and it will therefore pass through both coils, resulting in an efficient transformer. In the ideal case 100% of the flux is delivered to the second coil. Transformer circuit symbols usually consist of back-to-back coil/inductor symbols corresponding with the windings. Lines between the coils may be used to indicate the type of core material. Some examples are shown in Fig.3. Fig.2 indicates the direction of the input current and induced voltage. In order to use the transformer correctly it is often necessary to know which way round the connections are. This is indicated by using dots on the device and on the schematic symbols, known as phasing dots. The dotted terminals have the same instantaneous voltage polarity – when the dotted primary is being driven by the positive half of the AC cycle the dotted secondary will have a positive polarity with respect to the non-dotted terminal. A ir core Ferrite/ metal pow d er core Metal (iron) core Fig.3. Transformer symbols – note the cores and phase dots. Practical Electronics | June | 2021 Transformers During the positive cycle the current will flow into the dotted primary terminal and out of the dotted secondary. Inductors and transformers 𝑁𝑁! A coil on 𝑣𝑣its own 𝑣𝑣is# an inductor. In fact, a ! = 𝑁𝑁 straight wire has" inductance, but usually an inductor component is formed from one or more loops (turns) of insulated Primary and secondary coil turns wire (sometimes very many turns). The The relationship between the primary and # related to the number inductance (L)𝑁𝑁is secondary voltage for an ideal transform 𝑖𝑖! = 𝑖𝑖# 𝑁𝑁 ! (N2), but the specific of turns squared is determined by the relative number of turns in each winding. Specifically, for a relationship depends on the type, structure primary voltage (vp) applied to a winding and dimensions of the inductor. In general, we can write L = kN2 so N = √(L/k) for a with NP turns, and a secondary with NS &𝑁𝑁! ⁄type 𝑁𝑁# (𝑣𝑣and 𝑣𝑣# 𝑣𝑣 𝑁𝑁!% of structure, 𝑁𝑁!%where k size turns the secondary voltage will be: # ! given 𝑅𝑅$ = = = ) an *ideal ) *transformer = ) % * 𝑅𝑅$& we % is a constant. For 𝑖𝑖! 𝑁𝑁# 𝑖𝑖# 𝑁𝑁# &𝑁𝑁# ⁄𝑁𝑁! (𝑖𝑖# 𝑁𝑁! can assume k is the same for the primary 𝑣𝑣! = 𝑣𝑣# 𝑁𝑁" and secondary windings, so substituting into the voltage relationship above we get: The secondary voltage is the primary voltage multiplied by the turns ratio. This 𝐿𝐿# +𝐿𝐿# ⁄𝑘𝑘 relationship applies to both the rms and 𝑣𝑣! = 𝑣𝑣# = . 𝑣𝑣# 𝑁𝑁# 𝐿𝐿! peak +𝐿𝐿! ⁄𝑘𝑘 𝑖𝑖! =values 𝑖𝑖# of the voltages. If the turns ! ratio is 𝑁𝑁 larger than 1 then the secondary The turns ratio is equal to the square root voltage will be larger than the primary and of the inductance ratio of the windings we have a step-up transformer. The other (considered as individual inductors). This way round is a step-down transformer. % 𝑣𝑣# 𝑣𝑣! &𝑁𝑁! ⁄𝑁𝑁 𝑁𝑁!is 𝑁𝑁!%used inductance ratio is important for setting The commonly # (𝑣𝑣#latter & in linear 𝑅𝑅$ = = = ) % * ) * = ) % * 𝑅𝑅$ up transformers in SPICE simulations. power supply 𝑖𝑖! 𝑁𝑁# 𝑖𝑖circuits 𝑁𝑁to &𝑁𝑁# ⁄𝑁𝑁 # # obtain a low ! (𝑖𝑖# Transformers are not simply inductors voltage from the mains supply. – the discussion above indicates that A transformer transfers power from an ideal transformer with a resistor primary to secondary. An ideal transformer connected to the secondary looks like is 100% efficient so the input power will 𝐿𝐿# power, for primary and +𝐿𝐿# ⁄𝑘𝑘the output a resistor to the source. The inductance equal 𝑣𝑣! = 𝑣𝑣#! = . 𝑣𝑣# 𝑁𝑁 𝐿𝐿! of transformers does matter though, as it secondary (ip and is) we have 𝑣𝑣! ⁄=𝑘𝑘 𝑣𝑣#currents +𝐿𝐿 𝑁𝑁 affects circuit behaviour and performance. power vsi"s = vpip. From the turns equation However, it is of less importance in some above, this implies the current in the applications such as mains transformers. secondary is: If the degree to which the primary and 𝑁𝑁# secondary are coupled is not perfect, 𝑖𝑖 = 𝑖𝑖 ! # Transformers 𝑁𝑁! then the transformer will behave as part transformer and part inductor – this is Thus, a step-down transformer will take 𝑁𝑁! 𝑣𝑣! =primary 𝑣𝑣# than is referred to as leakage inductance. Another less current from the 𝑁𝑁 important non-ideal characteristic is the delivered via the secondary." For example, % 𝑣𝑣# vs = 𝑁𝑁 𝑣𝑣! &𝑁𝑁! ⁄𝑁𝑁 𝑁𝑁!% and resistance of the windings – ideally, this if# (𝑣𝑣 vp# = 240V 12V (turns ratio ! & 𝑁𝑁 𝑅𝑅$ = = ! = ) % * ) * = ) % * 𝑅𝑅$ 𝑣𝑣!𝑖𝑖!= &𝑁𝑁 𝑣𝑣## ⁄𝑁𝑁 is zero, but wires in real transformers 20:1) and 1A is taken from the secondary 𝑁𝑁 𝑖𝑖 𝑁𝑁 (𝑖𝑖 # # # ! # 𝑁𝑁" will have some resistance. The many the current in the primary will be 50mA 𝑁𝑁# properties of the core are also important (1/20A). 𝑖𝑖! = 𝑖𝑖# ! ) across the in real transformers – one important but If we connect a resistor𝑁𝑁(R L complex factor is core saturation, which secondary, Ohm’s law tells us that vs/is = RL. 𝑁𝑁# +𝐿𝐿# ⁄𝑘𝑘the turns𝐿𝐿ratio # is a limit on the maximum magnetic flux relationships, we get: 𝑖𝑖! = 𝑣𝑣𝑖𝑖#= Using 𝑣𝑣# = . 𝑣𝑣# 𝑁𝑁! ! 𝐿𝐿! leading to often undesirable outcomes +𝐿𝐿! ⁄𝑘𝑘 𝑣𝑣! &𝑁𝑁! ⁄𝑁𝑁# (𝑣𝑣# 𝑁𝑁!% 𝑣𝑣# 𝑁𝑁!% & as waveform distortion. (The one 𝑅𝑅$ = = = ) % * ) * = ) % *such 𝑅𝑅$ 𝑖𝑖! 𝑁𝑁# 𝑖𝑖# 𝑁𝑁# exception to this effect demonstrates &𝑁𝑁# ⁄𝑁𝑁! (𝑖𝑖# Fig.4. Two inductors in LTspice – not a transformer! an advantage of the otherwise weak performance of air-cored inductor – they do not saturate.) Working with LTspice Simulating transformers in LTspice is not as straightforward as other passive components such as resistors and capacitors – we cannot simply drop a transformer symbol onto the schematic. A transformer is made up of two or more coils, so we can draw a transformer symbol by suitably placing two inductors on the schematic, as shown in Fig.4. The symbols can be reflected and rotated using the Ctrl-E and Ctrl-R keys, but it may also be necessary to use the move tool to change the position of the label and value to get the transformer looking right. Fig.4 has a 100Hz, 1V sinewave driving a ‘transformer’ comprising two 1H inductors. The transformer should have a 1:1 ratio, so it should output 1V, but if we simulate this circuit, we will get no output signal, as shown in Fig.5. The problem is that as far as LTspice is concerned we just have two completely separate coils with no relationship between them. We have to tell LTspice that they form a transformer. This is done by declaring the two inductors to be a mutual inductance, which requires a statement to be placed on the schematic. As you may know, the real input to the simulator is not the schematic drawing but the netlist obtained from it. A netlist is a text description of the circuit plus commands to instruct the simulator what to do. It is generated automatically, but 𝑁𝑁! ⁄𝑁𝑁# (𝑣𝑣# 𝑁𝑁!% 𝑣𝑣# 𝑁𝑁!% = ) % * ) * = ) % * 𝑅𝑅$& 𝑁𝑁# 𝑖𝑖# 𝑁𝑁# 𝑁𝑁# ⁄𝑁𝑁! (𝑖𝑖# 𝐿𝐿 ⁄𝑘𝑘 𝐿𝐿# Where R'L = vp𝑣𝑣/i! p=is+ the# effective resistance 𝑣𝑣# = . 𝑣𝑣 𝐿𝐿 # ⁄ 𝑘𝑘 +𝐿𝐿 of the primary as seen by ! the source !driving it. Thus, the transformer has changed the 𝐿𝐿# +𝐿𝐿# ⁄𝑘𝑘 value of the load resistor to (Np2/ 𝑣𝑣! = 𝑣𝑣# = .effective 𝑣𝑣# 𝐿𝐿 2 +𝐿𝐿! ⁄𝑘𝑘 N!s )RL. If a resistor RL is connected to the secondary of an ideal transformer then the transformer will look like a resistor of value R'L to the source driving the primary. This argument can be applied more generally to impedances (circuits with capacitance and inductance as well as resistance) connected to the secondary. This property of the transformer has uses in impedance matching. Practical Electronics | June | 2021 Fig.5. Simulation results from the circuit in Fig.4. 59 inductors have initial letter K – the perhaps more obvious M, or T for transformer are already taken by MOSFETs and transmission lines. The syntax of the mutual inductance statement is: Fig.6. Adding the mutual inductance statement. Fig.7. LTspice transformer circuit. you can view it from the menu using View > Netlist. For Fig.4, the netlist is: L1 In 0 1 L2 Out 0 1 V1 In 0 SINE(0 1 100) .tran 100m .backanno .end All of this can be set up via drawing or through menu operations (the .tran simulation command is generated via the Edit Simulation Cmd menu item). The .backanno and .end commands are automatically added to every netlist. It should be obvious what .end is for. The .backanno command causes data to be stored that facilitates probing for currents by clicking on schematic symbol pins. To create a transformer we need to add a mutual inductor component to the netlist, but this cannot be done directly via the menus. We have to add the netlist line for a mutual inductor as text to the schematic. All components start with a specific initial letter (L for inductor, V for voltage source and so on). Mutual [L3 ...] This is a name starting with K, followed by the list of inductors which are coupled together (the windings of the transformer), followed by the coupling coefficient. For ideal transformers the coupling coefficient is 1, but this parameter can be set in the range 0 to 1 to model transformers where not all of the magnetic flux perfectly links the coils (the non-coupled part forms the leakage inductance). Circuit behaviour can be complex for non-unity coupling coefficients, may result in slow simulations, and is often not necessary. It is recommended that simulations are first run with a coupling coefficient of 1, even if other values are to be investigated later. For the circuit in Fig.4, we need: K1 L1 L2 1 To add the mutual inductance statement to the schematic use the Spice Directive (.op) menu item (see Fig.6). Make sure the SPICE directive option is selected (not the comment) or it will not work. Place the text by clicking on the schematic close to the transformer (see Fig.7). Note that once you have added the mutual inductance statement LTspice will automatically add the phasing dots to the schematic – reorientate the inductors if these are not the right way round for how you want your schematic drawn. Cores and coupling in LTspice The core lines (see Fig.3) are not part of the LTspice inductor symbol but can be added as additional graphic elements. This should be done using right-click > draw > line, not by drawing a wire. Drawing Fig.8. Simulation results for the circuit in Fig.7. 60 Kxxx L1 L2 <coefficient> Fig.9. Output phase changed with respect to the circuit in Fig.7. these as part of the transformer symbol will have no effect on the simulation. Although we may use an ideal coupling coefficient it is usually a good idea to include the winding’s series resistance in the simulation (ideally this is zero but will not be so for a real transformer). This can be measured or obtained from the transformer’s specification. For the circuit in Fig.7, we have added this to the voltage source, which means it can be displayed on the schematic, but this only works because we have a voltage source connected directly to the winding. Series resistance can also be added to the inductor directly by right clicking directly on the inductor symbol. However, this value is not displayed, which could be misleading. It can also be added as a separate resistor, which may in general be the best option. Simulating the circuit in Fig.7 produces the output shown in Fig.8 – the expected 1V signal. Fig.9 is the same as Fig.7, except the opposite end of the winding has been grounded (as indicated by the changed position of the phasing dot for L2. The resulting output is 180° (half a sinewave) out of phase with the input (see Fig.10 and compare with Fig.8). Inductance values for LTspice transformers The examples so far have used two equal inductors, so the input and output inductors are equal on the LTspice schematic. As the transformer in LTspice is configured from inductors there is no direct way to set the turns ratio – we have to set the ratio of the inductor values to the square of the transformers turns ratio. For example, if we want a step-up transformer with ratio 1:2 then we need an inductor ratio of 1:4. This is shown in the circuit in Fig.11. The resulting waveforms (Fig.12) show a 2V output for a 1V input. This raises the question of what inductance values to use in a real design – these examples just use round numbers for convenience. Obviously, if the inductance values are specified for a real device, then that indicates what to use. Otherwise, if you have a suitable meter (eg, a DC LRC meter) then the value can be measured Practical Electronics | June | 2021 Fig.11. Step-up transformer with 1:2 ratio. Fig.10. Simulation results for the circuit in Fig.9. (with the other windings open circuit). Failing this, the inductance should be chosen to give a sensible current (I) in the context of the circuit using I = V/ZL where V is the expected winding voltage and ZL is the impedance of the inductor at the operating frequency (f), found using ZL = 2πfL. Fig.12. Simulation results for the circuit in Fig.11. Real transformers have complex behaviours with significant non-ideal characteristics, which can make simulation (and circuit design) challenging. A key characteristic for simulation is the winding resistance that we have already mentioned, which should always be included to prevent excessive DC currents. DC currents clearly occur if DC is present in the defined input voltage, or as a result of the circuit’s behaviour, but may also occur less obviously due to the initial conditions used by the simulator at start-up. Ticking the ‘Skip initial operating point solution’ (uic) option for a transient simulation can help prevent problems caused by this. Leakage inductance can be modelled with additional inductors of the mutual inductor coupling coefficient. Modelling nonlinear effects due to the core saturation requires more complex equivalent circuits. ESR Electronic Components Ltd All of our stock is RoHS compliant and CE approved. Visit our well stocked shop for all of your requirements or order on-line. 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