From the Editor's Desk

Rectifier snubbing - background and Best Practices

MorganJones

Look inside almost any piece of commercial equipment having a linear power supply and you will findsmall capacitors across the rectifier diodes. Those capacitors are there to prevent the combination ofmains transformer leakage inductance and diode capacitance from ringing when the diode switches off.But would ringing really occur, and ifsnubbers do work, how well do they work?

To answer these questions, this article will first focus on investigating transformer leakage inductance,and then address semiconductor diyde capadtance. The two results are then applied to simulations.

Transformer leakage inductance

Transformers first convert electric current into magnetic flux, then convert that flux back '. ;ur-rent - with the benefit of electrical isolation and convenience of current/voltage trar m. If

the transformer was 100% efficient, all electrical power entering the primary would ^ole at

the secondary, but no transformer is lossless, and one loss is due to imperfect magne luplingbetween primary and secondary. Imperfect coupling is a problem in audio not just because it rep-resents power wastage but because leakageflux may induce currents in neighbouring circuitry lead-ing to audible hum. Further, eddy currents in the core consume power. The combined effect of fluxleakage and core losses is habitually represented by a series inductance known as the leakage in-ductance, as shown in Figure 1.

Perfect transformer

Figure 1 Simple high frequency transformer model.

Morgan JonesRectifier snubbing - background and Best Practices

Fam1^s^f^s.^^^°-

sIIE

104Frequency (Hz)

Fi^e2^'n9leakage,n^ancefran,aplcto^pedancea9a,nstfr^ency.

fourcoH;ponent.ode;^;^^S^N^^I-teted-PedanceoftheeTw^o2r^ndmodelcomponentvalues^^^^^^tanceoflT5rr,Hh^^ZZe^^^^!n^twhict1.point'theleaka9emd-=^r^^s;^^^^^^^.s::::sr:e;;:^^^^^^^^^^

Figure 3 Tapping a transformer-s leakage inductance to add loss resistance.

BelulwLarc mtercstedin the interaction between a rectifier and its tra-f-, we must meas-urethe.leakage.inductance seen looking into the secondaryrathe^ than prima^Tb'meas'ureleTk-19e^ctance!ookingintoasecondary'wesimPlyreversethePr^ousprocedure-we

a, see Figure 4..-circuit

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sfO

I

10-

102

101

10°

coutantR13VJ^ayel:^(Lund H mams xfo.rm_er' P'-imar/ shorted.Rshunp650Q, L1»26tiH, L2»35»iH, C^un^536pF,'R;^91'mQI lul Lcu'

10-1

10-2

Measurement- Model

101 102 103 104 1Q5Frequency (Hz)

Fi9we41mpedance against frequency due to secondary leakage inductance.

10e 107

If,Flgureldidn'tdemonstrate the futilityofattempting to determine inductance from a single fre-quencymeasurement'Figure 4 should-Not onlyis there a m^" resonance at 1;1MHzfollo^d"t.mlnorresonances:but there is a kink in the risin9 resPonse c^^ around 6kHz that-necessitate"dthe six component tapped inductance model from Figure 5.

irnhaTdLre three common contemporaryforms ^""-^ction for the small mains transformers usedEl layer-woundToroidal

El split bobbin

Morgan Jones Rectifier snubbing - background and Best Practices

RS,;enes L2yrm__l

L1

R1

F?shunt-I-I-

Cshunt

Figure 5 Combining tapped leakage inductance with the original four component model.

We have already seen an El layer-wound transformerand might expect a toroidal transformerto havelower leakage inductance because of its good coil geometry and near-ideal construction. Figure 6~

Farn^ll 143-^0 ^5y^30VA tproid mains xformer, primary shorted.Rseries"1.77Q, R^1.95S1, L,^H, L^S^ C,hunt"170pF,1 R's'^^620<n Lcu-

a'

s(0

1Q.E

Frequency (Hz)Figure 6 Toroidal mains transformer.

In practte, this toroid is surprisingly similar to the previous El layer-wound transformer, with identi-cal low frequency leakage inductance (61 |iH) and multiple resonances after its main"1.7MHz~reso-nance.

We would expect a split bobbin El transformer to have high leakage inductance due to its deliber-ately poor coil geometry, as shown in Figure 7.

Farnell 141-487 12V split bobbin El mains xformer, primary shorted.Rshunt"3.56kQ, Li"125p.H, Ly470yM, Cshunt"24pF, Rseries"357mn

sc(D

I

104

103

10^

101

10"

10-1

101 102 10J 104 10b 10b 107Frequency (Hz)

Figure 7 El split bobbin.

The split bobbin El transformer meets expectations by having low frequency leakage inductance(595^iH) almost an order of magnitude higher than the preceding transformers. However, the en-forced low capacitance to the primary significantly attenuates resonances beyond the 1.3MHz mainresonance.

Surprisingly, these detailed measurements of the three constructions show that the simple model ofleakage inductance and series resistance represents a low voltage winding quite well up to about1 MHz, despite wildly different values for leakage inductance and shunt capacitance.The source of the=s400kHz inflection is unclear.

I had hoped that by measuring transformers of different constructions and secondary voltages Imight be able to offer an empirical formula for estimating leakage inductance, but after measuringtwenty transformers, nothing firm could be deduced from the results. If we need to quantify an iron-cored transformer's leakage inductance, only a series of impedance measurements will do.

Measuring impedance against frequency

Although a dedicated impedance analyser certainly speeds measurement, the cost of an analyserthat measures >200kHz is prohibitive. Fortunately, a cheap function generator and digital oscillo-

scope having automated measurements can do the job quite well as is shown in Figure 8.

1011

Morgan Jones Rectifier snubbing - background and Best Practices

SYNC,

OSC 'Y' CHANNEL

OSC EXT TRIG

Figure 8 This simple set-up enables impedance to be measured over a wide range.

The function generator's open circuit sinusoidal output voltage Vou. is set to its maximum and meas-ured before connecting to the transformer.

The function generator drives the transformer's secondary via a 2.2kQ series resistance. The oscillo-scope ilextemally tri9gered from the 9enerator's tri99er °utP"t and measures VRMS and frequencyacross the transformer secondary. The transformer's primary is short-circuited. The measurement'sare averaged over 32 traces to increase accuracy.

Amplitude measurements are then made at various frequencies and recorded in a spreadsheet as afunction of frequency. The function generator's output resistance and 2.2kQ series resistance form"th^upper-'e90f.a potential divider'and becausethe generator voltage is known, the output voltage isknown, and as the source resistance is known, the load impedance can be calculated.''

Although 2.2kQ is suggested as a series resistance, the real requirement is that the series resistanceshould cause th!transformer vdta9e at --"onance to be roughly half the generator's open"drcu7tout_put.volta9e:Derived rcsult accuracy suffers as this volta9e is exceeded be""se small changes'inamplitude imply progressively larger impedance changes. Conversely, if the voltage at resonance'is!oosmall'-denved result accuracy suffers as signals fa"into the noise floor-The ideal methodology is.touse,avariableresistance'quicl<lysweepfrequencywhilstobservingtransformervoltage,adjust"thevariable resistance to achieve roughly halfopen-circuit amplitude'across the transfome7at'reso'--lanre'replace the variable rcsistance with the nearest convenient standard value, and then performthe formal measurement sweep.

My wideband measurements were made <20kHz with my Hameg 8118 LCR bridge, but >20kHzmeasurements were achieved using the function generator and oscilloscope technique.

Leakage indudance summary

Although a useful theoretical concept, leakage inductance can only be determined accurately byfit-ting a model to measurement results of an impedance sweep against frequency.

From low frequencies to a little above resonance, the impedance deviation between optimum modeland measurement using the four component model is usually within ±30%, and sometimes as littleas ±5%, whereas the six component model can invariably be fitted to within ±10% and sometimes±1%.

Determining transformer model values is not an end in itself - we require those values for an AC sim-ulation. 30% impedance deviation corresponds to 3dB error, whereas 1 0% deviation corresponds to<1 dB error. Thus, a carefully obtained six component model enables subsequent AC simulation hav-ing <1 dB error, and therefore believable results.

Silicon diode depletion capadtance

When a semiconductor diode is reverse biased, a depletion region devoid of current carriers formsbetween the two contacts. The contacts have non-zero area and are either side of an insulator, cre-

ating capacitance (& = 12 for silicon). It is well-known that the thickness of the depletion region is pro-portional to the square root of applied voltage, and this property is exploited in varicap (variablecapacitance) diodes for tuning radios. Semiconductor manufacturer data sheets [2] commonly in-elude graphs ofcapacitance against reverse voltage, as in Figure 9.

10kHz SOmVRMs capacitance, 1N4007 (a=36, b=-0.5, c=2.9pF)

siiQ.

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Reverse bias (V)

Figure 91 N4007 capacitance against reverse bias.

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Morgan Jones

Figure 9 shows measurement overlaid with modelled capaci tance:

'(PF) +2.9

^. ,0 sho». c.pactanc. <or»f.,.sl_could me.su,;;A,~;h.7:;:^., *", ,^.^ ",:wo graphs. Figure 10, and Figure 11, are enlightening.

Silicon diode 10kHz SOmViRMS

ssu

IG

31DQ10 .Z- -11DQ10STTA512F1N4007 :- ---

-1 -0.5Forward bias (V)

Fi9urew^P^ncecomparisonofSchottky(31DQW,11DQW).softrecovery(STTA5,2F).rectifiers.

and standard (1 N4007)

Rectifier snubbing - background and Best Practices

Silicon diode 10kHz SOmVRMs-

ss~w<A£ 10^c3^in

-1.5 -1 -0.5Forward bias (V)

0.5

Figure 11 Shunt resistance comparison ofSchottky (31DQ10,11DQ10), soft recovery (SJTA5 12F), and standard(1N4007)rectifiers.

Radio receivers, redifier diode capadtance, and transformer leakage indudance

We have investigated transformer leakage inductance and semiconductor diodes. It is now time totake the results of those two investigations and combine them in an LTspice model.To do this, we ini-

tially make some simplifying assumptions:

We are only interested in behaviour at the transition between the diode switching on and off.

. The transformer can be represented by a single leakage inductance and series resistance.

The first assumption returns us to our original question of whether or not rectifier diode capacitance

can cause transformer leakage inductance to ring. The second assumption is used to avoid the pos-sibility that a particular transformer's six component model might uniquely tip the results one wayor the other.

The model tests a 1 2V power supply using an El split bobbin transformer (therefore having high leak-age inductance and low stray capacitance), standard 1 N4007 diodes in a centre-tapped rectifier (and

therefore only one diode in series at any one time), into a 15,000|^F reservoir capacitor, loaded by aregulator (which is a constant current load, and therefore provides no damping); Figure 12.

14

15

Morgan Jones Rectifier snubbing - background and Best Prartices

12V .ft-1N4007

12V1N4007

-t^J

=^15000uF

Figure 12 Simple power supply using full-wave rectifier.

?"VT"intoan LTSPice model (Figure 13) requircs the additio" "fparasitic components to the^servoir capacitor, such as SOmQ equivalent series resistance, and 20nH series inductance. Becausewlarc-only_interested in behaviour when the diode is off'we represe"t the diode a7depletion"c7-pacitanceandshunt resistance. We representthetransformerasavoltagesourceinserieTwithleak-age inductance and series resistance.

Transformer

520uH

Diode

Rshuntf-\ -I-

Capacitor

-'depletion

400m0hm ;

|30m0hm

;20nH

=^15000uF

Figure 13 LTspice model of Figure 12.

16

We use a 1V interference source in order that the numerical results should directly represent atten-uation, and perform six tests using different depletion capacitances and shunt resistances selectedfrom the previously measurements at different diode voltages. Figure 14.

Unsnubbed 1N4007 diode plus 520^H leakage inductance

-120IxlO3 5xl05 IxlO6

Frequency (Hz)5xl06 IxlO7

Figure 14 Modelled response ofunsnubbed 1 N4007 plus 520^iH leakage inductance for various diode voltages.

Figure 14 is far less alarming than at first appears. The fact that LTspice could produce a frequency

sweep without crashing answers the first of our questions at the beginning of this article - this trans-former doesn't ring. Judging from this explicit investigation and my previous experience, it appearsthat a faulty transformer is required to provoke ringing.

However, what Figure 14 does show is that as the rectifier diode switches, it tunes a resonant circuit

through the medium and long wave broadcast bands, and since mains wiring is an effective aerial atthese frequencies, that can't be good, so we typically snub the 1 N4007 diode with a 47n capacitor,

Figure 15.

Figure 15 shows that a 47nF snubbing capacitance replaces the sweep through broadcast bandswith a slightly attenuated but stationary peak at 32kHz. Worse, a low voltage transformer (<20V) willdefinitely be inductive at such a low frequency, so the peak will occur.

Rather than connecting an arbitrarily large capacitor across each diode, perhaps we could be a lit-tie more scientific and choose an optimum value? A good value might be five times depletion ca-

pacitance, but as 1 N4007 capacitance changes viciously with voltage, what might work? Well, youhave to start somewhere, and I had plenty of 1 nF capacitors. Having chosen a capacitance that will

17

Morgan Jones

18

0

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Badly snubbed (47nF, Oft) 1N4007 diode plus 520^H leakage inductance.

-100

-120

+0.4V ! -I - - +0.3V |

+0.2V |-j --- 0V I

- -0.5V |---- -IV

10000 30000 50000 70000Frequency (Hz)

Figure 15 Typical capacitor-only snubbing.

90000

swamp diode capacitance for most of its range, we can calculate the Q of the resulting resonantcircuit using:

0-£/?Vc

Alternatively, we could state that we require Q = 0.707 (maximally flat response) and ,equation:

R= 10.707 ^C

2x520x10-61x10-9

"1/(Q

Theequation suggests that the resonance formed bythediodesnubbercapadtanceandtransformerleakage inductance could be damped by 1 k0 series resistance, so we add'this to the model and'theresult of analysing this appears in Figure 16.

Notethat^ot only does a damped smaller snubber caPadta"ce leave the resonance further awayfrom the audio band, but it reduces its amplitude by >40dB, rendering it entirely negligible. Notealso that there is still a momentary (heavily damped) resonance at 1 OOkHzjust before thediodecon^ducts, due to the very high 1 N4007 capacitancejust before conduction.

Rectifier snubbing - background and Best Practices

Correctly snubbed (InF, Ikft) 1N4007 diode plus 520p.H leakage inductance

0

+0.4V+0.3V+0.2Vov-0.5V-IV

-12010s 10e

Frequency (Hz)

Figure 16 Correctly snubbed 1 N4007 diode plus 520iJiH leakage inductance.

Schottkydiodes

Schottky diodes are a popular (although expensive) substitution for the low voltage 1 N4001 .TTie argu-

ment runs that because conduction in a Schottky diode relies on electrons (rather than holes), there isno current overshootto cause ringing. I substituted a 31 DQ1 0 Schottky diode into the model. Figure 17.

Unsnubbed 31DQ10 Schottly diode plus 520^H leakage inductance

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Figure 17 Unsnubbed Schottkyplus 520pH leakage inductance.

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Morgan Jones Redder snubbing - background and Best Practices

The reason that Figure 23 shows no peak is as follows. Resonance between diode capacitance andtransformer secondary can only occur at frequencies where secondary impedance is inductive. Ifdiode capacitance is low, the theoretical resonant frequency combined with leakage inductance isabove the transformer's own self-resonant frequency, the transformer appears capacitive, cresonance cannot occur.

Finally, the full six component model for the 12V El split bobbin transformer first seen in Figure 7 wasmodelled with the results presented in Figure 24.

Unsnubbed 1N4007 diode plus 12V El split bobbin six component model

m-0^^

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I

-20

-40

-60

-80

-100

-120 .-=105 106

Frequency (Hz)107

Fi9we24Notethatdespitetheabsenceofanexplicitsnubber,thereisonlyahintofthesweptresonanceproblemseen in Figure 14.

Thetransformerin Figure 24 is on the cusp of exhibiting swept frequency resonance and might ben-efit from^a carefully damped snubber. Note that because a full six component transforme'r modelwas-used' pl"s a dlode model including chan9in9 depletion capacitance and leakage resistance,-Fig-ure 24 is expected to be a close approximation to reality below 2MHz.

Snubber position

The traditional position for the diode snubbers is across the diodes - they're treated as being switchesacting upon an inductance, so for a bridge rectifier, we need four snubbers. But Figure 24 impliesS!"werea!!yn-!ed to do is to make the transformer's leaka9e inductance look less inductive^byadding a parallel Zobel network. Perhaps we should change snubber position slightly and"fit a sin/-gle snubber/Zobel network across the transformer secondary?

1N4007 diode plus snubbed (InF, Ikn) 12V El split bobbin six component model

-12005 106

Frequency (Hz)

Figure 25 A single snubber directly across the trans former tames leakage inductance.

107

As hoped. Figure 25 shows that the snubber works in its new position, with a saving of six compo-nents (assuming bridge rectifier); secondaries for centre-tapped rectifiers need two snubbers (one

from each winding end to the centre tap). More significantly, it transpires that the new position makesit almost impossible to select snubber values that degrade performance, as witnessed by Figure 26.

EZ81: snubbers across xformer, and unsnubbedRseries"127n, Ri"19.2mH, Ry^.SSmH, Cshuntsa!1nF, Rshunt"18kfi

CD.o

<uT334-1

Q.E<

-20

-40

-60

-80

-100

-120

-140

-160

unsnubbed

InF,Ikn33pF, 47kn

104 105Frequency (Hz)

Figure 26 Once the snubber is across the transformer, its values become uncritical.

10e

2425

Morgan Jones

The EZ81 had previously been degraded 16dB by adding a snubber, but even applying wholly inap-propriate snubber values (1 nF, 1 k) across either the simple LR or six component transformer sec-ondary improved rather than degraded performance.

Conclusions

We have been chasing a demon that doesn't exist, then made matters worse by having the wrongparts in the wrong place - and too many of them. A single damped snubber/Zobel across each trans-former secondary is all we need to suppress the swept resonance problem. Ideally, we would knowdiode capacitance, measure leakage inductance and calculate the correct resistance to set Q = 0.7,but even if we don't, 1 nF and 1 k will almost certainly do in both high and low voltage supplies.

References

[1]Wilson P R, "Effective Modelling of leakage Inductance for use in Circuit Simulation"[2] Vishay Semiconductors, "1 N4001 thru 1 N4007 (General Purpose Plastic Rectifier)"

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