Transformers - Revision history

Lewispaul: Reverted edits by Lewispaul (talk) to last revision by Analogspiceman

2020-05-17T17:14:22Z

Reverted edits by Lewispaul (talk) to last revision by Analogspiceman

Lewispaul: /* Transformers */

2020-05-17T17:13:18Z

‎Transformers

Lewispaul: /* I want to model leakage inductance - how should I do that? */

2020-05-17T17:09:11Z

‎I want to model leakage inductance - how should I do that?

Analogspiceman: /* Now how do I plot a B-H curve to see the Chan model's hysteresis-saturation curves? */

2019-11-21T04:48:06Z

‎Now how do I plot a B-H curve to see the Chan model's hysteresis-saturation curves?

Analogspiceman: /* Transformers */ corrected typos, clarified some text

2019-11-20T20:29:07Z

‎Transformers: corrected typos, clarified some text

Analogspiceman: /* Transformers */ updated graphics + minor edits

2019-11-19T14:49:39Z

‎Transformers: updated graphics + minor edits

Analogspiceman: /* Transformers */ reorganized and update for Chan core in process

2019-11-15T21:57:47Z

‎Transformers: reorganized and update for Chan core in process

Analogspiceman: /* Chan Transformer (saturating magnetizing inductance with hysteresis - limited energy storage) */

2019-11-15T21:30:21Z

‎Chan Transformer (saturating magnetizing inductance with hysteresis - limited energy storage)

Analogspiceman: /* Chan Transformer (saturating magnetizing inductance with hysteresis - limited energy storage) */

2019-11-15T12:21:32Z

‎Chan Transformer (saturating magnetizing inductance with hysteresis - limited energy storage)

Analogspiceman: /* I want to model leakage inductance - how should I do that? */ added comments about the difference between leakage inductance of a winding versus of a transformer

2019-11-15T11:41:04Z

‎I want to model leakage inductance - how should I do that?: added comments about the difference between leakage inductance of a winding versus of a transformer

← Older revision		Revision as of 17:14, 17 May 2020
Line 44:		Line 44:
	K1 L1 L2 0.2		K1 L1 L2 0.2

		+	[[File:Loosely_Coupled_Equivalent.gif\|right\|185px\|(full: 370x312)\|"Winding" inductance is 1H]]

	* In LTspice, this is the same as:		* In LTspice, this is the same as:

← Older revision		Revision as of 17:13, 17 May 2020
Line 44:		Line 44:
	K1 L1 L2 0.2		K1 L1 L2 0.2

−	~~<img href=ltwiki.org/images/f/ff/Loosely_Coupled_Equivalent.gif>~~

	* In LTspice, this is the same as:		* In LTspice, this is the same as:

@@ Line 44: / Line 44: @@
   K1  L1 L2  0.2
-[[File:Loosely_Coupled_Equivalent.gif|right|185px|(full: 370x312)|"Winding" inductance is 1H]]
+<img href=ltwiki.org/images/f/ff/Loosely_Coupled_Equivalent.gif>
 * In LTspice, this is the same as:

@@ Line 160: / Line 160: @@
 ''Under construction.''
-ampere∙turns/meter       = 4∙π/1000 Oersted(Oe)
+ampere∙turn/meter       = 4∙π/1000 Oersted(Oe)
 volt∙seconds/turn/meter² = 1 Tesla(T) = 10,000 gauss(G)

@@ Line 42: / Line 42: @@
   L1   1  0  1H
   L2   2  0  1H
-  K12 L1 L2  0.2
+  K1  L1 L2  0.2
 [[File:Loosely_Coupled_Equivalent.gif|right|185px|(full: 370x312)|"Winding" inductance is 1H]]
 * In LTspice, this is the same as:
-  L1   1  m  0.8H
+  L1   1 12  0.8H
-  Lm   m  0  0.2H
+  L12 12  0  0.2H
-  L2   2  m  0.8H
+  L2   2 12  0.8H
 Other engineering conventions regarding the definition of K, coupling and formula for leakage inductance are irrelevant to LTspice.&nbsp; Other formula for leakage inductance are intended to find total leakage inductance from an input winding through to an output winding(s) rather than the partial leakage inductance for each individual winding.
@@ Line 57: / Line 57: @@
 Yes, LTspice comes with a non-linear hysteretic core model built in!&nbsp; This is the 1991 model by John Chan et al.&nbsp; Compared to older core models, [[the Chan model]] is particularly robust, computationally efficient and compact, requiring only three parameters to define most any commonly encountered magnetic hysteresis loop.&nbsp; (LTspice also allows building an arbitrary inductance based on self flux and/or any valid function of node voltages and branch currents.&nbsp; [[The Arbitrary Inductor model|The arbitrary inductor model]] can be very efficiently used to create saturation without hysteresis.)
-Once the core material's generic magnetic properties are set, establishing the circuit-level non-linear inductance requires specifying three more parameters to set the geometry of the specific core and specifying one additional parameter for the core winding turn-count.&nbsp; The Chan inductor <font color="green" title="(has been mentioned as a possibility for a future release)">does not currently</font> directly support [[Mutual Inductance]], so unless only a single-winding inductor is being modeled, multiple windings must be added via additional circuitry.&nbsp; The simplest way to do this is to construct an ideal, unity coupled transformer with as many windings as required and then put the Chan inductor directly in parallel with any one of the windings (taking care to set the turns to match that particular winding).&nbsp; Since the magnetic effects (including non-saturated inductance) are already modeled by the Chan inductor, the inductance of the transformer's parallel winding must be enough larger (>>10) not to significantly load the Chan inductance.&nbsp; As before, the inductances for the other windings should be scaled by the square of their individual turns ratios (with respect to the paralleled winding).
+Once the Chan core material's generic magnetic properties are set, establishing the circuit-level non-linear inductance requires specifying three more parameters to set the geometry of the specific core and specifying one additional parameter for the core winding turn-count.&nbsp; The Chan inductor <font color="green" title="(has been mentioned as a possibility for a future release)">does not currently</font> directly support [[Mutual Inductance]], so unless only a single-winding inductor is being modeled, multiple windings must be added via additional circuitry.&nbsp; The simplest way to do this is to construct an ideal, unity coupled transformer with as many windings as required and then put the Chan inductor directly in parallel with any one of the windings (taking care to set the turns to match that particular winding).&nbsp; Since the magnetic effects (including non-saturated inductance) are already modeled by the Chan inductor, the inductance of the transformer's parallel winding must be enough larger (>>10) not to significantly load the Chan inductance.&nbsp; As before, the inductances for the other windings should be scaled by the square of their individual turns ratios (with respect to the paralleled winding).
 === Okay, but calculating winding inductances is tedious.&nbsp; Is there some way to just enter a turns count for all the windings? ===
@@ Line 84: / Line 84: @@
 === DC to DC Transformer (no magnetizing inductance - no energy storage) ===
-The transformer winding subcircuits are DC coupled and, when connected to a "core" (1TΩ in parallel with 1pF) that supports DC without drawing current, they combine to make a transformer that draws no magnetizing current, stores no energy and therefore is immune to errant initial conditions.&nbsp; This may be an advantage when first experimenting with new power circuits.
+The transformer winding subcircuits are DC coupled and, when connected to a "core" (1TΩ in parallel with 1pF) that supports DC without drawing current, they combine to make a transformer that draws no magnetizing current, stores no energy and therefore is immune to errant initial conditions.&nbsp; This model may be an advantage when first experimenting with new power circuits.
 For better cosmetics the simple DC core may encapsulated in its own subcircuit and symbol.&nbsp;
@@ Line 102: / Line 102: @@
 === Linear Transformer (linear magnetizing inductance - potentially unlimited energy storage) ===
-A standard linear transformer may easily be created simply by changing the core to a standard inductor with Rs=0.&nbsp; In this form (with a standard ''linear'' magnetizing inductance "core") the model is mostly useful as a perceptual window into the way coupled inductors work in LTspice since linear transformers are more easily and simply built with standard coupled inductors.&nbsp; Note that the magnetizing inductance "core" is the single summing point for the ''ampere-turns'' from all the windings and is the sole source of ''impressed voltage'' (=L*di/dt) reflected onto all the windings.&nbsp; Although this subcircuit is an unnecessary and overly complex representation for a transformer with a linear core inductance, it will be absolutely required if multiple windings are to be "wrapped" onto LTspice's nonlinear Chan inductance model, so take a moment to read it through (the Chan version will follow shortly).
+A standard linear transformer may easily be created simply by changing the core to be a standard inductor with Rs=0.&nbsp; In this form (with a standard ''linear'' magnetizing inductance "core") the model is mostly useful as a perceptual window into the way coupled inductors work in LTspice since linear transformers are more easily and simply built with standard coupled inductors.&nbsp; Note that the magnetizing inductance "core" is the single summing point for the ''ampere-turns'' from all the windings and is the sole source of ''impressed voltage'' (=L*di/dt) reflected onto all the windings.&nbsp; Although this subcircuit is an unnecessary and overly complex representation for a transformer with a linear core inductance, it will be absolutely required if multiple windings are to be "wrapped" onto LTspice's nonlinear Chan inductance model, so take a moment to read it through (the Chan version will follow shortly).
@@ Line 130: / Line 130: @@
 === Chan Transformer (saturating magnetizing inductance with hysteresis - limited energy storage) ===
-Now that the windings are separate from the core, a Chan inductor may simply be substituted for the linear inductor core.  Since the inductance of a  Chan is not assigned, but is determined by its magnetic material, dimensional properties and winding turns, one must adjust inductance by iteratively adjusting the gap and/or winding turns.
+Now that the windings are separate from the core, a Chan inductor may simply be substituted for the linear inductor core.&nbsp; Since the inductance of a Chan inductor is not assigned, but is determined by its magnetic material, dimensional properties and winding turns, one must adjust inductance by iteratively adjusting the gap and/or winding turns.&nbsp; Measure inductancs by comparing slopes when subjected to the same stepped DC voltage.

@@ Line 11: / Line 11: @@
 === How do I make a transformer in LTspice? ===
-[[File:LTspice_Transformer.gif|right|174px|Two lines were used to draw the core]]
+[[File:LTspice_Transformer.gif|right|179x143px|Two lines were used to draw the core]]
 Although it is very possible to make a dedicated subcircuit for a specific transformer, the preferred method of making a generic transformer when drafting a simulation schematic is to simply place a separate inductor for each separate transformer winding and then couple them all together magnetically via a single ''[[Mutual Inductance]] (K) statement'' placed as a [[SPICE Directive]] on the schematic.&nbsp; Note that inductors called out in a [[Mutual Inductance]] statement will be automatically given a phasing dot if one does not already exist.
@@ Line 36: / Line 36: @@
 For n inductors coupled together with a K statement, each inductor L1 through Ln is divided into two parts, a completely non-coupled "leakage" inductance equal to (1-K)*Lx (where Lx is the particular inductor in question) and a completely coupled "mutual" inductance equal to K*Lx.&nbsp; Voltage and current ratios of the coupled parts are related by the ratio of the square root of the the inductances L1 through Ln (this is the apparent "turns ratio").
 * For example, given two inductors coupled by a K statement:
-[[File:Loosely_Coupled_Transformer.gif|right|153px|Coupling is only K=0.2]]
+  L1   1  0  1H
-  L1 1 0 1H
+  L2   2  0  1H
-  L2 2 0 1H
+  K12 L1 L2  0.2
-[[File:Loosely_Coupled_Equivalent.gif|right|182px|"Winding" inductance is 1H]]
+[[File:Loosely_Coupled_Equivalent.gif|right|185px|(full: 370x312)|"Winding" inductance is 1H]]
 * In LTspice, this is the same as:
-  L1 1 m 0.8H
+  L1   1  m  0.8H
-  Lm m 0 0.2H
+  Lm   m  0  0.2H
-  L2 2 m 0.8H
+  L2   2  m  0.8H
 Other engineering conventions regarding the definition of K, coupling and formula for leakage inductance are irrelevant to LTspice.&nbsp; Other formula for leakage inductance are intended to find total leakage inductance from an input winding through to an output winding(s) rather than the partial leakage inductance for each individual winding.
@@ Line 63: / Line 64: @@
 * Use parameters to to convert input of winding turns to inductance:
-[[File: Parameterized_Transformer.gif|right|304px|Turns are entered as parameters from which the inductance is calculated]]
+[[File: Parameterized_Transformer.gif|right|307px|(full: 613x236)|Turns are entered as parameters from which the inductance is calculated]]
   .param Lp=20m Np=200 Ns=20 ; inputs: primary inductance, primary turns, secondary turns
   .param  Kn=Lp/Np**2        ; calculated inductance per turn squared
@@ Line 73: / Line 74: @@
 * First, the basic winding: Start (dot), Finish, Core:
-[[File: Simple Winding Symbol & Subcircuit.gif|right|479px|This simple subcircuit is equivalent to an inductor or transformer winding]]
+[[File: Simple Winding Symbol & Subcircuit.gif|right|480px|(full: 959x270)|This simple subcircuit is equivalent to an inductor or transformer winding]]
   .subckt Winding s f c params: n=100 L=1u Rs=1m Rp=100
   Lw s 1 {L} Rser={Rs} Rpar={Rp} ; leakage and resistance
@@ Line 87: / Line 88: @@
 For better cosmetics the simple DC core may encapsulated in its own subcircuit and symbol.&nbsp;
-[[File: DC_to_DC_Transformer.gif|right|190px|DC to DC (because of "core") transformer with two windings]]
+[[File: DC_to_DC_Transformer.gif|right|188px|(full: 376x288)|DC to DC (because of "core") transformer with two windings]]
 * Here is a DC "core" that does not draw increasing current with time:
   .subckt Core_DC C
@@ Line 93: / Line 94: @@
   .ends Core_DC
-[[File: DC_to_DC_Transformer_&_Core.gif|right|189px|DC to DC transformer with DC core symbol for aesthetics]]
+[[File: DC_to_DC_Transformer_&_Core.gif|right|186px|(full: 372x266)|DC to DC transformer with DC core symbol for aesthetics]]
 * DC-to-DC Transformer Equivalent (Netlist Uprocessed):
   Xp P 0 C Winding n=1 L=1u Rs=1m Rp=100 ; primary winding of 1:1 transformer
@@ Line 105: / Line 106: @@
 * Parametize and wrap an inductor with a subcircuit:
-[[File: Linear_Core.gif|right|191px|A linear core is simply an inductor with Rser=0]]
+[[File: Linear_Core.gif|right|212px|(full: 423x165)|A linear core is simply an inductor with Rser=0]]
   .subckt Core_Linear C params: L=20m Rp=10k Cp=10p
   Lc C 0 {L} Rser=0 Rpar={Rp} Cpar={Cp}
   .ends Core_Linear
-[[File: Linear_Transformer.gif|right|176px|Transformer with linear core]]
+[[File: Linear_Transformer.gif|right|187px|(full: 374x270)|Transformer with linear core]]
 * Linear Transformer Equivalent (Netlist Unprocessed):
   Xp P 0 C Winding n=1 L=1u Rs=1m Rp=100 ; primary winding of 1:1 transformer
@@ Line 117: / Line 118: @@
 * Linear Transformer Equivalent (Netlist Flattened):
-[[File: Linear_Transformer_Full.gif|right|438px|Transformer with linear core]]
+[[File: Linear_Transformer_Full.gif|right|455px|(full: 909x236)|Transformer with linear core]]
   Lp Ps  1 1u Rser=1m Rpar=100   ; leakage and resistance
   Ep  1 Pf  C  0  1              ; impose core volts/turn*turns onto winding
@@ Line 133: / Line 134: @@
 * Parametize and wrap a Chan inductor with a subcircuit:
-[[File: Chan_Core.gif|right|167px|Physical properties based core with hysteresis and saturation]]
+[[File: Chan_Core.gif|right|170px|(full: 340x288)|Physical properties based core with hysteresis and saturation]]
   .subckt Core_Chan C params:
   + Bs=0.4 Br=0.1 Hc=20       ; Core default magnetic parameters
@@ Line 144: / Line 145: @@
   .ends Core_Chan
-[[File: Chan_Transformer.gif|right|167px|Physically parameterized transformer with hysteresis and saturation]]
+[[File: Chan_Transformer.gif|right|172px|(full: 344x276)|Physically parameterized transformer with hysteresis and saturation]]
 * Chan Transformer Equivalent (Netlist Unprocessed):
   Xp P 0 C Winding n=100 L=1u Rs=1m Rp=100 ; primary winding of 1:1 transformer

@@ Line 81: / Line 81: @@
-==== DC to DC Transformer (no magnetizing inductance - no energy storage) ====
+=== DC to DC Transformer (no magnetizing inductance - no energy storage) ===
 The transformer winding subcircuits are DC coupled and, when connected to a "core" (1TΩ in parallel with 1pF) that supports DC without drawing current, they combine to make a transformer that draws no magnetizing current, stores no energy and therefore is immune to errant initial conditions.&nbsp; This may be an advantage when first experimenting with new power circuits.
@@ Line 99: / Line 99: @@
   Xc C CoreDC ; subcircuit consisting of 1TΩ in parallel with 1pF
-==== Linear Transformer (linear magnetizing inductance - potentially unlimited energy storage) ====
+=== Linear Transformer (linear magnetizing inductance - potentially unlimited energy storage) ===
 A standard linear transformer may easily be created simply by changing the core to a standard inductor with Rs=0.&nbsp; In this form (with a standard ''linear'' magnetizing inductance "core") the model is mostly useful as a perceptual window into the way coupled inductors work in LTspice since linear transformers are more easily and simply built with standard coupled inductors.&nbsp; Note that the magnetizing inductance "core" is the single summing point for the ''ampere-turns'' from all the windings and is the sole source of ''impressed voltage'' (=L*di/dt) reflected onto all the windings.&nbsp; Although this subcircuit is an unnecessary and overly complex representation for a transformer with a linear core inductance, it will be absolutely required if multiple windings are to be "wrapped" onto LTspice's nonlinear Chan inductance model, so take a moment to read it through (the Chan version will follow shortly).
@@ Line 127: / Line 127: @@
   Ls Ss  1 1u Rser=1m Rpar=100   ; leakage and resistance
-==== Chan Transformer (saturating magnetizing inductance with hysteresis - limited energy storage) ====
+=== Chan Transformer (saturating magnetizing inductance with hysteresis - limited energy storage) ===
 Now that the windings are separate from the core, a Chan inductor may simply be substituted for the linear inductor core.  Since the inductance of a  Chan is not assigned, but is determined by its magnetic material, dimensional properties and winding turns, one must adjust inductance by iteratively adjusting the gap and/or winding turns.
@@ Line 153: / Line 153: @@
   +  Rp=10k Cp=10p                         ; Assigned core parallel loss and capacitance
-==== Now how do I plot a B-H curve to see the Chan model's hysteresis-saturation curves? ====
+=== Now how do I plot a B-H curve to see the Chan model's hysteresis-saturation curves? ===
 Plotting hysteresis-saturation curves of the Chan Transformer in LTspice

@@ Line 159: / Line 159: @@
 </pre>
 And here is the same thing using parameters within curly braces to give value to LTspice's extended inductors and to a coupling statement (mutual inductance).&nbsp; Note that there is no need to create a subcircuit with this method because Lp and Ls can be placed directly on the schematic as symbols and K1 and the .param statement may be placed as SPICE text (this is the section of netlist that would then result).&nbsp; The prior subcircuit form (or something like it) only becomes necessary in conjunction with a custom two-winding transformer symbol or if a nonlinear core (magnetizing inductance) model must be used.
 <pre>

@@ Line 31: / Line 31: @@
 === I want to model leakage inductance - how should I do that? ===
-The most flexible method is to keep the windings' mutual inductance statement at unity and add a small discrete leakage inductance in series with each winding.&nbsp; This is the most straightforward way to model transformers with asymmetrical leakage inductances.&nbsp; However, if your transformer is electrically symmetrical, it may be more convenient to simply set the mutual inductance to a value less than one.&nbsp; For each winding the resulting leakage inductance will be (1-K) times that winding's inductance.&nbsp; Note that each winding's coupled inductance also will decrease to K times that winding's inductance, but for typical values of K (>>0.9) this effect will be very small.
+The most flexible method is to keep the windings' mutual inductance statement at unity and add a small discrete leakage inductance in series with each winding.&nbsp; This is the most straightforward way to model transformers with asymmetrical leakage inductances.&nbsp; However, if your transformer is electrically symmetrical, it may be more convenient to simply set the mutual inductance to a value less than one.&nbsp; For each winding the resulting leakage inductance will be (1-K) times that winding's inductance.&nbsp; Also, each winding's coupled inductance also will decrease to K times that winding's inductance, but for typical values of K (>>0.9) this effect will be very small.&nbsp; Note that physical transformer leakage inductance measured in the laboratory typically is close to the sum of the leakage inductance of two windings in series combination (with coupled inductance and perhaps several windings partially in parallel).
-This is how LTspice "sees" coupled inductors:
+'''This is how LTspice "sees" coupled inductors:'''
 For n inductors coupled together with a K statement, each inductor L1 through Ln is divided into two parts, a completely non-coupled "leakage" inductance equal to (1-K)*Lx (where Lx is the particular inductor in question) and a completely coupled "mutual" inductance equal to K*Lx.&nbsp; Voltage and current ratios of the coupled parts are related by the ratio of the square root of the the inductances L1 through Ln (this is the apparent "turns ratio").
@@ Line 50: / Line 50: @@
   L2 2 m 0.8H
-Other engineering conventions regarding the definition of K, coupling and formula for leakage inductance are irrelevant to LTspice.&nbsp; Other formula for leakage inductance are intended to find total leakage inductance from an input winding through to an output winding(s) rather than for each individual winding.
+Other engineering conventions regarding the definition of K, coupling and formula for leakage inductance are irrelevant to LTspice.&nbsp; Other formula for leakage inductance are intended to find total leakage inductance from an input winding through to an output winding(s) rather than the partial leakage inductance for each individual winding.
 === How about transformer saturation effects?&nbsp; Can LTspice model those? ===