Method for Calculating the Pulse Load of Zener Diodes in Intrinsic Safety for Zener Barriers Using the Melting Integral and Cold Resistance and Their Issues

Zener Barriere 705x262 1

Introduction

In the devel­op­ment of intrin­si­cal­ly safe devices, the pre­cise cal­cu­la­tion of the pulse load on Zen­er diodes is essen­tial, par­tic­u­lar­ly for devices oper­at­ing with mains volt­age. The abil­i­ty to cor­rect­ly assess such pulse loads ensures that the Zen­er diodes oper­ate with­in their safe oper­at­ing lim­its, thus main­tain­ing the integri­ty of the entire device. This blog post intro­duces a method for cal­cu­lat­ing the pulse load that takes into account the melt­ing inte­gral and cold resis­tance. Although this method doesn’t ful­ly align with phys­i­cal real­i­ties, it is a known prac­tice applied by devel­op­ers and man­u­fac­tur­ers of intrin­si­cal­ly safe devices, as well as by cer­ti­fi­ca­tion bod­ies for ATEX or IECEx approval. There are sev­er­al points of crit­i­cism regard­ing this method, which will be dis­cussed in this arti­cle. Many thanks for the com­ments and sug­ges­tions on this top­ic. In case of doubt, it is advis­able to con­duct prac­ti­cal test­ing or seek fur­ther infor­ma­tion from the man­u­fac­tur­er of the diodes and fus­es.

The Importance of Pulse Load

Con­sid­er­ing pulse load is of cru­cial impor­tance, espe­cial­ly for devices pow­ered by mains volt­age. The Zen­er diodes in such bar­ri­ers are often pro­tect­ed by a fuse. How­ev­er, since fus­es are rel­a­tive­ly slow in response to tran­sient events, the diodes can be exposed to pulse cur­rents. If these loads are not accu­rate­ly cal­cu­lat­ed and con­sid­ered, it could lead to diode fail­ure and, in the worst case, a safe­ty haz­ard. There­fore, a pre­cise and reli­able method for cal­cu­lat­ing the pulse load is nec­es­sary to ensure the safe­ty and reli­a­bil­i­ty of the devices.

00058 837542461 1500x1000 1

The Melting Integral

The melt­ing inte­gral, also known as the i²t val­ue or lim­it load inte­gral, is a mea­sure of the short-term over­load capa­bil­i­ty of elec­tri­cal or elec­tron­ic com­po­nents under pulsed loads. It describes how a fuse reacts to such a load: Once the i²t val­ue is reached, the fuse will melt and inter­rupt the cir­cuit.

The i²t val­ue spec­i­fied in the datasheet serves for select­ing the fuse and only indi­cates the ener­gy at which the fuse wire starts to melt (melt­ing i²t). After the wire has melt­ed, there is a peri­od dur­ing which an arc is sus­tained (arc­ing i²t). Only after this peri­od is over will the fuse open. The total time, also known as the clear­ing i²t, is not pro­vid­ed in the datasheet.

Fur­ther infor­ma­tion can be found in the “Fuse­ol­o­gy Design Guide” by Lit­tel­fuse.

Fuse­ol­o­gy – Lit­tel­fuse

Cold Resistance

The cold resis­tance of a fuse is the ohmic resis­tance, usu­al­ly spec­i­fied at room tem­per­a­ture. Since the fuse wire is typ­i­cal­ly made of a met­al that behaves as a pos­i­tive tem­per­a­ture coef­fi­cient con­duc­tor, its resis­tance increas­es as it heats up. The cold resis­tance is the val­ue when the fuse is not car­ry­ing cur­rent. In nor­mal oper­a­tion, the val­ue is high­er as the fuse heats up due to the cur­rent flow.

In the case of a short-dura­­tion volt­age pulse, the ohmic resis­tance acts as a cur­rent lim­iter and can reduce the pulse cur­rent.

00007 3975483988

Introduction of the Parameters Used

Calcpad

The fol­low­ing para­me­ters must be known in order to car­ry out the cal­cu­la­tion pre­cise­ly:

Uz_max = 19 V·1.05 = 19.95 V

Max­i­mum Zen­er volt­age: The volt­age at which the Zen­er diode oper­ates in the break­down mode, tak­ing tol­er­ances into account. Exam­ple: OnSe­mi 1N5356B

 

IR = 5.3 A @8.3ms

The pulse cur­rent is spec­i­fied as the max­i­mum per­mis­si­ble non-repet­i­­tive rec­tan­gu­lar cur­rent with a pulse width (PW) of 8.3 ms.

 

SF1.5 = 1.5

Safe­ty fac­tor of 1.5 to com­ply with the 2/3 cri­te­ri­on accord­ing to EN IEC 60079–11

 

SFfuse = 1.7

Safe­ty fac­tor of 1.7 to be applied when using the rat­ed cur­rent.

 

Um_peak = 253 V·  √ 2 = 357.8 V

Max­i­mum peak volt­age per­mit­ted at the input of the bar­ri­er.

 

IF1n = 50 mA

Rat­ed cur­rent of the fuse

 

Rcold_F1 = 11.34 Ω

Rat­ed cur­rent of the fuse (Exam­ple: Lit­tel­fuse 242.125)

 

I2tfuse_F1 = 0.000103 A2·s

Melt­ing inte­gral of the fuse (Exam­ple: Lit­tel­fuse 242.125)

 

Calculation of continuous power

Calcpad

Pz_const = IF1n·SFfuse·Uz_max = 50 mA·1.7·19.95 V = 1695.75 mW

To cor­rect­ly size the Zen­er diode, a safe­ty fac­tor of 1.5 must be applied to ensure that the diode is not loaded with more than 2/3 of its allow­able pow­er dis­si­pa­tion.

Pz_const_SF = Pz_const·SF1.5 = 1695.75 mW·1.5 = 2543.63 mW

 

 

The calculation of pulse load

Calcpad

The max­i­mum pulse cur­rent is cal­cu­lat­ed from the peak volt­age and the cold resis­tance. It is impor­tant to con­sid­er that for an alter­nat­ing cur­rent, the peak val­ue must first be cal­cu­lat­ed. For a direct cur­rent, the defined max­i­mum input volt­age applies.

 

Ipulse = Um_peakRcold_F1 = 357.8 V11.34 Ω = 31.55 A

 

 

tpulse = I2tfuse_F1Ipulse2 = 0.000103 A2·s(31.55 A)2 = 103.46 ns

 

The pulse volt­age across the Zen­er diode is lim­it­ed by the max­i­mum Zen­er volt­age. The max­i­mum Zen­er volt­age may be high­er at high pulse cur­rents than the max­i­mum val­ue spec­i­fied in the datasheet. The volt­age drop across the dif­fer­en­tial resis­tance is added to the max­i­mum volt­age. How­ev­er, this dif­fer­en­tial resis­tance is not spec­i­fied in the datasheet for such high cur­rents and decreas­es with increas­ing cur­rent. It is pos­si­ble to deter­mine the Zen­er volt­age at pulse cur­rent through the test for “Deter­mi­na­tion of loose­ly spec­i­fy­fied Para­me­ters.” The fol­low­ing cal­cu­la­tions will use the max­i­mum Zen­er volt­age with­out con­sid­er­ing the dif­fer­en­tial resis­tance. Since volt­age, cur­rent, and time are now spec­i­fied, the ener­gy of the pulse dis­si­pat­ed in the diode can be cal­cu­lat­ed using these para­me­ters.

 

Epulse = Uz_max·Ipulse·tpulse = 19.95 V·31.55 A·103.46 ns = 65.13 μJ

 

The per­mis­si­ble ener­gy of the diode must be obtained from the datasheet. In this case, it is cal­cu­lat­ed based on the max­i­mum surge cur­rent, which is spec­i­fied as 5.3 A for a dura­tion of 8.3 ms.

 

Ez_pulse_permitted = Uz_max·IR·8.3 ms = 19.95 V·5.3 A·8.3 ms = 877.6 mJ

 

In this case, it is evi­dent that the ener­gy of the pulse is sev­er­al mag­ni­tudes small­er than the per­mis­si­ble lev­el.

00048 837542461 1500x1000 1

Conclusion

The cal­cu­la­tion of the pulse load of Zen­er diodes is a nec­es­sary endeav­or when fus­es are used to pro­tect them. This pro­ce­dure is also described in the cur­rent Edi­tion 7 of IEC 60079–11. Cer­tain­ly, some assump­tions and inter­pre­ta­tions of the val­ues from the datasheets are nec­es­sary, which can be crit­i­cized in detail. In par­tic­u­lar, the use of the melt­ing inte­gral in this man­ner is not cor­rect.

It is advis­able to obtain fur­ther infor­ma­tion from the com­po­nent man­u­fac­tur­ers or deter­mine the para­me­ters through test­ing. IEC 60079–11 offers the pos­si­bil­i­ty of deter­min­ing a val­ue based on 10 sam­ples, which is not pro­vid­ed in the datasheet.

Fur­ther pro­tec­tive mea­sures are also con­ceiv­able, such as pro­tect­ing the diodes from high­er pulse cur­rents by using a resis­tor in series with the fuse. Addi­tion­al­ly, cal­cu­lat­ing the pow­er of the pulse can be ben­e­fi­cial if the diodes have a max­i­mum pulse load spec­i­fied in watts in the datasheet.

Leave a comment

Cat­e­gories: Eigen­sicher­heit — Berech­nun­gen
Autor:
ich scaled

Stef­fen Scholle

Share

Related Posts