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Telecommunications Industry Association TR41.9-06-02-008 Document Cover Sheet Project Number Document Title Type A Surge Generator Tolerance Source Bourns Ltd. Contact Name: Mick Maytum Complete Address: Bourns Ltd., Manton Lane, Bedford, MK41 7BJ, UK Distribution TR-41.9 Intended Purpose of Document (Select one) X Phone: +44 7879 697652 Fax: +44 8700 521810 Email: [email protected] For Incorporation Into TIA Publication For Information Other (describe) - The document to which this cover statement is attached is submitted to a Formulating Group or sub-element thereof of the Telecommunications Industry Association (TIA) in accordance with the provisions of Sections 6.4.1–6.4.6 inclusive of the TIA Engineering Manual dated March 2005, all of which provisions are hereby incorporated by reference. Abstract This contribution analyses CR and L/R rise-controlled capacitive discharge generator designs. The waveshape tolerance is controlled by generator component tolerances and the ratio (a) of external to internal discharge currents. For CR rise-controlled capacitive discharge generator designs the output resistor split () has a major influence on the rise time tolerance. The proposed tolerance values are: 10/160 200 A –0 +30 A, 10 µs +0 –5 µs/ 160 µs -0 +50 µs 1500 V –0 +150 V, 10 µs +0 –3 µs/ 160 µs -0 +100 µs 10/560 100 A –0 +15 A, 10 µs +0 –5 µs/ 560 µs -0 +150 µs 800 V –0 +80 V, 10 µs +0 –3 µs/ 560 µs -0 +300 µs v1.0 – 20050426 Telecommunications Industry Association TR41.9-06-02-008 Type A Surge Generator Tolerance – A Mathematical Analysis 1 Introduction Much of the content here was published either as Applications I nformation in Bourns TISP® data sheets or submissions to NIPP-NEP (T1E1.7 that was). This contribution analyses CR and L/R rise-controlled capacitive discharge generator designs. The waveshape tolerance is controlled by generator component tolerances and the ratio () of external to internal discharge currents. Those short of time should skip to clauses 9, Summary Table, and 10, Comments and Proposals. 2 Generator Categories There are three categories of surge generator having defined open -circuit and short-circuit waveshapes: single waveshape, combination waveshape and circuit defined. Single waveshape generators have the same nominal waveshape for the open -circuit voltage and short-circuit current (e.g. <10/>160 open-circuit voltage and short-circuit current). Combination generators have two waveshapes, one for the open-circuit voltage and the other for short-circuit current (e.g. 1.2/50 open-circuit voltage and 8/20 short-circuit current) Circuit specified generators usually equate to a combination generator (e.g. the Type B surge generator that gives an 9/720 open-circuit voltage and a 5/320 short-circuit current). If the combination or circuit -defined generators operate into a finite resistance the waveshape produced is intermediate between the open-circuit and short-circuit values. 3 Waveshape and Waveform Notation Most lightning tests, used for equipment verification, specify a unidirectional waveform that has defined peak amplitude with an exponential rise and an exponential decay. Waveshapes are classified in terms of rise time in microseconds and a decay time in microseconds to 50% of the peak amplitude. The notation used for the waveshape is rise time/decay time, without the microseconds quantity and the “/” between the two values has no mathematical sign ificance. A 50A, 5/320 waveform would have a peak current value of 50 A, a rise time of 5 µs and a decay time of 320 µs. 3.1 Waveshape Rise and Decay Definition Current waveshape rise time is normally expressed as a line drawn through the 10 % to 90 % rising edge points extrapolated to the 0 (virtual zero time) and 100 % levels. The current decay time is measured from the virtual zero time until the current has decayed to 50 % of the maximum amplitude. Voltage waveshapes are normally expressed in one of two wa ys. As the rising edge of the voltage often has ringing, the voltage rise time is expressed as a line drawn through the 30 % to 90 % rising edge points extrapolated to the 0 (virtual zero time) and 100 % levels. The second way is to use the current waveshape method with a line drawn through the 10 % to 90 % rising edge points extrapolated to the 0 (virtual zero time) and 100 % levels (Telcordia GR 1089-CORE, Issue 3 Annex A). In both voltage waveshape cases, the voltage decay time is measured from the virtual zero time until the current has decayed to 50 % of the maximum amplitude. Page 2 Telecommunications Industry Association TR41.9-06-02-008 VOLTAGE WAVEFORM DEFINITION CURRENT WAVEFORM DEFINITION 90 90 80 80 70 70 60 60 Amplitude % 100 Amplitude - % 100 50 40 30 20 10 50 40 30 20 10 0 VIRTUAL FRONT TIME VIRTUAL ORIGIN 0 VIRTUAL TIME TO HALF VALUE VIRTUAL FRONT TIME VIRTUAL ORIGIN VIRTUAL TIME TO HALF VALUE IEC 60099-1 (1994) Designation of impulse shape: A combination of two numbers, the first representing the virtual front time (T1) and the second the virtual time to half value of the tail (T2). It is written as T1/T2, both in microseconds, the sign "/" having no mathematical meaning. Figure 1 Current Waveshape and 30% to 90 % Voltage Waveshape 3.2 Waveshape Rise and Decay times from Surge Generator Circuit Time Constants 3.2.1 Rise time When a single CR or L/R time constant, , controls the waveshape rise time, the 10 % to 90 % method gives a rise time of 2.75. The 30 % to 90 % method gives a rise time of 3.24 . Thus the two methods of measurement do not give the same value for the same rise waveshape, as the mathematical treatment assumes a linear and not an exponential rise. 3.2.2 Decay time When a single CR constant, , controls the waveshape decay time, the decay time is given by 0.697. 4 Generator Components People who build their own generators have the problem of fin ding reliable, high-voltage, highcurrent components. A 2 kV, 100 µF capacitor is hard to find and often the most economic capacitance tolerance will be ±10 %. Small value capacitors, used for rise time control, may be obtained with ±5 % values. Resistors can normally be obtained in ±5 % values. These tolerance values will be used for the circuit calculations. 5 Type A Surge Waveforms 5.1 Metallic, >800 V, 100 A, <10/>560 Waveform Applied between any pair of connections on which lightning surges may occur. 5.1.1 Open-circuit Voltage The surge shall have an open-circuit voltage waveform with minimum peak amplitude of 800 V, a maximum 30 % to 90 % method rise (front) time of 10 µs and a minimum decay time of 560 µs. Page 3 Telecommunications Industry Association 5.1.2 TR41.9-06-02-008 Short-circuit Current The surge shall have an short-circuit current waveform with minimum peak amplitude of 100 A, a maximum 10 % to 90 % method rise (front) time of 10 µs and a minimum decay time of 560 µs. 5.2 Longitudinal, >1500 V, >200 A, <10/>160 Waveform Applied to any pair of connections on which lightning s urges may occur. 5.2.1 Open-circuit Voltage The surge shall have an open-circuit voltage waveform with minimum peak amplitude of 1500 V, a maximum 30 % to 90 % method rise (front) time of 10 µs and a minimum decay time of 160 µs. 5.2.2 Short-circuit Current The surge shall have an short-circuit current waveform with minimum peak amplitude of 200 A, a maximum 10 % to 90 % method rise (front) time of 10 µs and a minimum decay time of 160 µs. 6 Generator Circuits There are two common types of generator circuit; CR rise time controlled and L/R rise time controlled. 6.1 CR Rise Time Controlled Generator Figure 2 shows a CR rise time controlled generator and the two circuit simplifications used to calculate the decay and rise times. VC R2 SW R1 C1 R3 C2 CR Rise Time Controlled Generator VC C1 R2 SW R3 R1 R2 R3 C2 Decay Time Circuit Rise Time Circuit Figure 2. CR rise time controlled generator circuits Page 4 Telecommunications Industry Association TR41.9-06-02-008 The energy storage capacitance, C 1 , and the circuit shunt resistance control the waveshape decay time. The shunt resistance is resistor R 1 for the open-circuit output condition and resistor R 1 in parallel with the series combination of resistors R 2 and R 3 for the short-circuit output condition. In the open-circuit output case, capacitor C 2 and resistor R 2 control the rise time. For shortcircuit output condition, capacitor C 2 and resistor R 2 and R 3 in parallel control the rise time. 6.2 LR Rise Time Controlled Generator Figure 2 shows a LR rise time controlled generator and the two circuit simplifications used to calculate the decay and rise times. VC L SW R2 R1 C1 L/R Rise Time Controlled Generator VC C1 R2 SW R1 L R2 R1 Decay Time Circuit Rise Time Circuit Figure 3. LR rise time controlled generator circuits The energy storage capacitance, C 1 , and the circuit shunt resistance control the waveshape decay time. The shunt resistance is resistor R 1 for open-circuit output condition and resistor R 1 in parallel with resistors R 2 for the short-circuit output condition. In the open-circuit output case, inductor L and resistor R 1 control the rise time. For short-circuit output condition, inductor L and resistor R 1 and R 2 in parallel control the rise time. Page 5 Telecommunications Industry Association 7 TR41.9-06-02-008 Decay Time t D Calculation The calculation will be done on the generic circuit of Figure 4. T SC = CSxa RO/(1+a ) T OC = CSxa RO RO CS a RO CS Short-Circuit Decay Time Circuit a RO Open-Circuit Decay Time Circuit Figure 4 Open- and Short-circuit Decay time constants R O is the resistance between the energy storage capacitor, C S , and the output. The ratio of external to internal discharge currents is defined as . This makes the energy storage capacitor internal shunt resistance R O . The minimum short-circuit decay time, t DSCMIN is given by: t DSCMIN = 0.697x0.9x0.95xC S xR O /(1+) The maximum open-circuit decay time, t DOCMAX is given by: t DOCMAX = 0.697x1.1x1.05xC S xR O Hence: t DOCMAX / t DSCMIN = 1.1x1.05x(1+)/(0.9x0.95) = 1.35(1+) The value of is critical to the waveshape tolerance. If were 0.1, the open-circuit voltage maximum tolerance would be +49 % and the short-circuit current maximum tolerance becomes +35 %. However, for every 100 A of short-circuit current, the capacitor would have to supply 1100 A of current. Thus would dramatically increase the capacitor size and cost. If was set to 0.3, the open-circuit voltage maximum tolerance becomes +76 % and the shortcircuit current maximum tolerance is still +35 %. Using a ±5 % capacitor, for an of 0.1, would give an open-circuit voltage maximum tolerance of +34 % and the short-circuit current maximum tolerance becomes +22 %. Similarly, for an of 0.3, the open-circuit voltage maximum tolerance is +59 % and the short-circuit current maximum tolerance is +22 %. The generator component tolerance controls short-circuit current tolerance. The generator component tolerance and the design value of controls open-circuit voltage tolerance. Page 6 Telecommunications Industry Association 8 8.1 TR41.9-06-02-008 Rise Time t R Calculation L/R controlled rise The calculation will be done on the generic circuit of Figure 5. t RSC = (1+a )L/(a RO) t ROC = L/(a RO) L L RO a RO a RO Short-Circuit Rise Time Circuit Open-Circuit Rise Time Circuit Figure 5 Open- and Short-circuit Rise time constants R O is the resistance connected to the output terminal. The internal shunt resistance is R O . The short-circuit condition will have the largest time constant and the open-circuit condition will have the smallest time constant. However there are different multipliers used to calculate the current and voltage rise times. The short-circuit current rise time, t R is given by: t RSC = 2.75x(1+)L/(R O ) For a = 0.1, t RSC = 3.03xL/(R O ) For a = 0.3, t RSC = 3.58xL/(R O ) The open-circuit rise time, t R is given by: t ROC = 3.24xL/(R O ) An value of 0.18 equalises the t RSC and t ROC values. Below 0.18, t RSC is the shortest rise time. Above 0.18, t ROC is the shortest rise time. For < 0.18 t RSCMIN /t ROCMAX = (0.9x0.95x2.75x(1+)L/(R O )/(1.1x1.05x3.24xL/(R O )) = (0.9x0.95/(1.1x1.05))x0.85x(1+) For > 0.18 t ROCMIN /t RSCMAX = (0.9x0.95x3.24xL/(R O ))/(1.1x1.05x2.75x(1+)L/(R O )) Page 7 Telecommunications Industry Association TR41.9-06-02-008 = (0.9x0.95/(1.1x1.05))x1.18/(1+) 8.2 CR controlled rise The calculation will be done on the generic circuit of Figure 6. t RSC = (1-b )CRxb RO) bR O t ROC = CRxb RO (1-b )R O bR O CR CR Short-Circuit Rise Time Circuit Open-Circuit Rise Time Circuit Figure 6 Open- and Short-circuit Rise time constants R O is the resistance connected to the output terminal. The rise shaping circuit splits R O into R O and (1-)R O . The shaping capacitor, C R , is connected between common and the resistors junction. The short-circuit condition will have the smallest time constant and the open -circuit condition will have the largest time constant. The short-circuit current rise time, t R is given by: t RSC = 2.75x(1-)C R xR O The open-circuit rise time, t R is given by: t ROC = 3.24xC R xR O The short-circuit condition will always have the shortest rise time. The rise time ratio is: t RSCMIN /t ROCMAX = (0.95x0.95)(2.75x(1-)C R xR O )/((1.05x1.05)x(3.24xC R xRO )) = ((0.95x0.95)/(1.05x1.05))x0.85x(1-) = 0.82x0.85x(1-) = 0.7x(1-) Table 1 shows how the resistor split ratio, , strongly controls the rise time ratio, t RSCMIN /t ROCMAX . Table 1 0.1 0.2 0.3 t RSCMIN / t ROCMAX 0.63 0.56 0.49 Tolerance % -37 -44 -51 0.4 0.5 0.6 t RSCMIN / t ROCMAX 0.42 0.35 0.28 Page 8 Tolerance % -58 -65 -72 0.7 0.8 0.9 t RSCMIN / t ROCMAX 0.21 0.14 0.07 Tolerance % -79 -86 -93 Telecommunications Industry Association TR41.9-06-02-008 The Type B surge generator uses a ratio of 0.375 for metallic testing and 0.545 for longitudinal testing. 9 Summary Table Table 2 uses the equations of clauses 7 and 8 to calculate the tolerance percentage of the wave shape. As an application example, consider the <10/>160 waveshape and the tolerance values shown in the blue text row (L/R rise controlled generator with a ±10 % capacitor tolerance and an of 0.3). Open-circuit voltage waveshape = 10 µs 0 % –33 %/160 µs 0 % +76 % = 10 µs +0 –3.3 µs/ 160 µs -0 +120 µs Short-circuit current waveshape = 10 µs 0 % –26 %/160 µs 0 % +35 % = 10 µs +0 –2.6 µs/ 160 µs -0 +56 µs Table 2 Generator Type Tolerance of C S , Energy Storage Capacitor % ±10 L/R rise controlled ±5 CR rise controlled t RSC is for = 0.5. For other values see Table 1 ±10 ±5 Ratio of External to Internal Current Open-Circuit Voltage Short-Circuit Current t ROC % t DOC % t RSC % t DSC % 0.1 -26 49 -31 35 0.2 -27 62 -26 35 0.3 -33 76 -26 35 0.1 -18 34 -23 22 0.2 -20 47 -18 22 0.3 -26 59 -18 22 0.1 -18 49 -65 35 0.2 -18 62 -65 35 0.3 -18 76 -65 35 0.1 -18 34 -65 22 0.2 -18 47 -65 22 0.3 -18 59 -65 22 Page 9 Telecommunications Industry Association TR41.9-06-02-008 10 Comments and Proposals 10.1 Amplitude The use of ±5 % resistors components to connect to the output terminal gives a 10 % possible amplitude variation in current. Add to that a voltage setting accuracy of 5 % and the output current variation is 15 %. The open-circuit voltage should be capable of be set within a 10 % range. 10.2 Decay Time If only 5 % components are considered in Table 2, the (rounded) decay time tolerance becomes +30 % for current and +60 % for voltage. 10.3 Rise Time If only 5 % components are considered in Table 2, the (rounded) rise time tolerance for L/R rise time controlled generators becomes -30 % for current and -30 % for voltage. CR rise time controlled generators show -70 % for current and -20 % for voltage at a value of 0.5. Changing the to 0.3 would give -50 % for current and -20 % for voltage. 10.4 Proposal The decay time tolerance is about +30 % for current and +60 % for voltage. The rise time tolerance is about -50 % for current and -30 % for voltage. The amplitude tolerance is +15 % for current and +10 % for voltage. 10.4.1 <10/>160 Proposal 200 A –0 +30 A, 10 µs +0 –5 µs/ 160 µs -0 +50 µs 1500 V –0 +150 V, 10 µs +0 –3 µs/ 160 µs -0 +100 µs 10.4.2 <10/>560 Proposal 100 A –0 +15 A, 10 µs +0 –5 µs/ 560 µs -0 +150 µs 800 V –0 +80 V, 10 µs +0 –3 µs/ 560 µs -0 +300 µs Page 10