How does transformer inductance quantity calculate? Why are each not identical?

How does transformer inductance quantity calculate? Why are each not identical?

[introduction] for instance novice engineer Zhang San still does not have very good understanding to the computation of transformer of switch power source, go consulting Li Sihe Wang Wu, next Li Si gave formula of a computation to give Zhang San, wang Wu also gave formula of a computation to give Zhang San. Next of the formulary in spirits that Zhang San gives according to two people respectively calculated rise, after numerate, the inductance amount that discovers two formulary computation come out is far from same, and differred many, be Li Si is opposite or Wang Wu is opposite after all?
 
I design switch power source to also have a few time, the novice that contacts switch power source is more also, and a question that the novice asks at most is how transformer is calculated, and a question that asks at most in transformer computation is, the feeling that mentions above measures different question. I am OK so say, want to have engineer of this interrogative power source only, so certain specification you are a novice, devise a method without what master transformer certainly. The inductance amount that actually two engineers computation comes out is not same it is very normal, I can say even, same the project differs to two and the engineer that has experience will calculate the word of transformer, the inductance quantity scarcely that computation of these two engineers comes out is same.
 
Why? Have more reason among them. We are with be being stimulated instead exemple, the feeling quantity that computational transformer must come out is done not have originally with rootlet greatly be opposite absolutely with the fault, the transformer that wants you only inputs voltage in lowest when power of the biggest output works, transformer magnetism core is not saturated, additional temperature can pass a barrier, the computational method that cannot say him is incorrect.
 
So old to the engineer of experience calculated transformer why do every receive a new project metropolis recount? The transformer that why to comparative with a power directly is used directly? Want namely essentially from theoretic make sure magnetism core is not saturated (of course among them still other thing needs to assure, but enough to this understanding the novice, ask old hand people excuse) .
 
I take the computation that method of a calculation will come to explain inductance is measured below! We take the computation that stimulates DCM instead to be exemple, above all according to conversation of energy, attainable:
 
How does transformer inductance quantity calculate? Why are each not identical?
 
Among them the inductance quantity that Lp is transformer former edge, ip is the peak value electric current that former edge inductance measures, p is power input of switch power source, t is the switch cycle of switch power source.
 
Next according to the definition, if one is added on inductance constant voltage, the electric current on inductance rises as time linear, attainable:
 
How does transformer inductance quantity calculate? Why are each not identical?
 
When stimulating DCM to calculate instead, we are inputted in lowest most when high-power is outputted, make sure the job is in the word of DCM, can make sure limits of whole input voltage and whole power limits are DCM.
 
We see formula one, formula is mixed in DCM only BCM (critical) when hold water, because progressive die type falls to still need to subtract the energy of an initiative electric current just is met,be equal to P*T, see next pictures please.
 
How does transformer inductance quantity calculate? Why are each not identical?
 
Next we see formula 2, 2 also have formula to hold water when DCM only, of course BCM also holds water) , should want to change Ip into △ Ip to just go below CCM mode, (only this formula establishs CCM, among them △ Ip=Ip-I1) .
 
How does transformer inductance quantity calculate? Why are each not identical?
 
As a result of two formula holds water in DCM only, of course BCM also holds water, so if two formula see the word of equation group, reach the feeling that come is measured, can make sure transformer is in limits of whole input voltage and limits of whole output power are in DCM. Two formulary equation groups, want solution to come out to must be less than solution of two unknown ability to come out.
 
Formula looks to mix below us again formulary 2 medium parameter:
 
Formulary one in, lp and Ip are unknown, p is power it is foregone, t is switch cycle it is fixed (T=1/f) .
 
Formulary 2 in, ip and Ip are unknown, vin is foregone (preamble has been mentioned calculate below lowermost input voltage) , d is OK of set, we are designed commonly voltage is inputted in lowest most sky comparing is occupied when high-power at 0.5, can take here for instance 0.45; If the Vin above is obtained,should do than lowermost input voltage so D is returned so that put additionally small, it is OK that this has fun at oneself are pushed calculate, f is fixed.
 
Two formula in equation group have two unknown number only, can solve for certain go out. Formula mixes formulary group of 2 solution equation is attainable:
 
How does transformer inductance quantity calculate? Why are each not identical?
 
Right now we can calculate inductance amount come out. We get evenly according to Fu Miao again below:
 
How does transformer inductance quantity calculate? Why are each not identical?
 
Notable is, formula has 4 times in CCM or BCM (BCM is critical condition, also be right now hold water) hold water, in DCM do not hold water, read the description of next graphs please:
 
How does transformer inductance quantity calculate? Why are each not identical?
 
Formulary 3 hold water in BCM and DCM, formulary 4 hold water in BCM and CCM.
 
If we formula 3 with formula 4 again couplet establishs solution equation group, take two formulary be mixed that establish a condition namely, the be mixed that establishs a condition is BCM critical. Group of equation of that that is to say sees the transformer parameter after coming out, in lowest input voltage Vin is fully loaded with below, because of formula 3 be inputted in lowest namely and come out in next computation completely, transformer just is in BCM condition.
 
Right now formulary 3 it is OK that with formula 4 couplets establish us Vor (reflection voltage) computation comes out.
 
After everybody knows to reflex voltage plan numerate, can come out computation of v/LIT all over the ground number. Right now we should be calculated only after v/LIT all over the ground number, the basic parameter of transformer is about the same. The computation of v/LIT all over the ground number should make sure transformer is not saturated namely.
 
How does transformer inductance quantity calculate? Why are each not identical?
 
V/LIT all over the ground number is right now OK also numerate. We review 4 formula now:
 
How does transformer inductance quantity calculate? Why are each not identical?
How does transformer inductance quantity calculate? Why are each not identical?
How does transformer inductance quantity calculate? Why are each not identical?
How does transformer inductance quantity calculate? Why are each not identical?
 
With a specific Vin, the lowest that uses above us inputs voltage, next these 4 formulary couplet establish reoccupy the transformer that computation comes out, that is to say just is in critical condition in the transformer when Vin is inputted. When be fully loaded with a test so actually, when the input voltage moves prep above this Vin (the Vin that uses when computation) , so transformer is entered for certain intermittent condition, when the input voltage is moved to under this Vin (the Vin that uses when computation) , so transformer enters successive state for certain. This is a kind of critical point computation transformer law.
 
So, if we come to Vin drive up calculate designedly when computation, for instance: Be calculated so with Vin=176, right now we are calculated with Vin=264, so the inductance of this chronometer numerate measures the inductance with certain original prep above, of course when Vin drive up, d should be reduced, this wants to notice, those who have fun at but oneself are computative, want transformer to be in only right now full range is not saturated, so the inductance quantity that computation comes out also is right, and different is critical point drive up.
 
The volume that so inductance measures is the on any account with bit more critical response just, be not pair of faults, you can decide critical point in 85V, so full range is intermittent, of course you think more intermittent if you still can continue Vin decide a bit lower, you also can decide critical point in 264V, full range is successive, of course you still think a bit more successive word still can continue decide Vin a bit taller, also can decide critical point in 220V (prep above 220 intermittent, under 220 successive) , this is informal you will decide, as long as not saturated, your transformer not miscalculate.
 
Remember: Inductance measures the on any account with main bit more critical response, critical point is higher, transformer is more successive, critical point is lower, transformer is more intermittent.
 
Although say, transformer wants only not saturated not miscalculate, but you must be evaluated how more appropriate, for instance power very the hour is in commonly intermittent more appropriate: Power is little, switch loss takes main loss, guide connect loss to take less important loss, a bit more intermittent can reduce switch loss; When power is greater compared continuously commonly appropriate: Power is great, switch loss takes less important loss, guide connect loss to take main loss, can reduce continuously guide a loss.
 
Hope to after all novice engineers read this article, be inspired somewhat, do not ask why to be measured according to computational inductance of Li Si easily low, the computational inductance volume according to Wang Wu is high, whose to who complex issue, do not have to the fault this is you only to comprehend insufficient still.
 
 

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