# Mathematically defining test pulse 2b of the ISO-7637-2 section 5.6.2 automotive test standard

Blog Post created by EdBrorein on May 3, 2017

There are a variety of electrical disturbance tests for conducting validation tests on automotive electronic devices defined by ISO-7637-2 and ISO-16750-2, and a variety of other comparable standards. Based on the latest revisions of these two standards, ISO-7637-2 incorporates disturbances mostly with very high speed rise or fall times of nanoseconds to microseconds, while ISO-16750-2 incorporates electrical disturbances having relatively slow rise and fall times, on the order of a 1 millisecond, in comparison. From my previous posting I had illustrated how several the electrical disturbances defined in ISO-16750-2 can be quickly and easily implemented.

The ISO-7637-2 disturbances having fast rise and fall times are primarily a result of voltage spikes created by switching inductive devices on and off, or electrical devices creating a stream of voltage spikes while active. One exception is test pulse 2b of ISO-7637-2 section 5.6.2, which addresses the electrical disturbance created by an electrical motor, like that of a blower motor within the heating and air conditioning system. When the motor is running and then the ignition is switched off, the motor will change over from consuming power to generating a relatively slow voltage pulse back onto the electrical system, until all the energy from its spinning mass is dissipated. Test pulse 2b is depicted in Figure 1.

Figure 1: Test pulse 2b of ISO-7637 section 5.6.2

For this particular test pulse the standard recommends using an arbitrary waveform generator driving a DC power supply/amplifier with an analog control input. This is sensible given its complex shape, consisting of a step drop followed by the motor regeneration energy pulse. To simplify the set-up here, a Keysight N7951A 20V, 50A, 1KW Advance Power System power supply was chosen, as it already has arbitrary waveform generation capabilities built in, negating the need for the separate arbitrary waveform generator. The N7900A series APS is depicted in Figure 2.

Figure 2: N7900A series Advanced Power System, 1KW and 2KW models

While the step portion of test pulse 2b is easy to define and generate, how does one define the motor regeneration pulse? There are a number of possible approaches:

• A piecewise linear model can be constructed to approximate the shape.
• Alternately, software tools are available that can generate a data file of points from a graphical image of the waveform.
• Finally, there is a mathematical expression that defines this waveform, referred to as a double exponential, which can be utilized once it is understood how to do so.

A double exponential is basically the difference of two exponentials having different time constants, as shown in the expression:

UDE = UA(e-K1t – e-K2t)

Where UA is the electrical system (alternator) voltage, K1 is the slow time constant related to td, the duration of the test pulse, and K2 is the fast time constant related to tr, the rise time of the test pulse.

The trick of making use of this mathematical expression is to figure out how to relate the constants in the expression to the test pulse values shown in Figure 1. It turns out that this is relatively straight forward for this application due to the large relative difference between test pulse 2b’s rise and duration times. The time constant for the slow exponential related to the duration time can be defined as:

K1 = (2.303/td) Where td is the duration time (for the 100% to 10% transition)

While the time constant for the fast exponential related to the rise time can be defined as:

K2 = (2.197/tr) Where tr is the rise time (for the 10% to 90% transition)

The important thing here is that this is valid for when td >> tr. As the ratio of the two times lessens then there is more interaction between the two exponentials, requiring some compensation be made, primarily adjusting for some loss in amplitude. The resulting exponential and double exponential waveforms are shown in Figure 3 using the double exponential expression, based on using the rise and duration times, and amplitude value given in Figure 1 for test pulse 2b.

Figure 3: Exponential and double exponential waveforms for implementing ISO 7637-2 test pulse 2b

To actually generate test pulse 2b, the arbitrary waveform generation and editing capabilities in the Keysight 14585A software were used to put together a sequence consisting of a voltage step followed by the double exponential we just mathematically defined. The 14585A is a companion software package used to set up and run the ARB, and then retrieve back, display and analyze measurements from the N7900A series Advanced Power System. The resulting test pulse waveform was run, captured and displayed in the 14585A’s scope mode, shown in Figure 4.

Figure 4: Test pulse 2b of ISO 7637-2 generated and captured using 14585A software

In closing, test pulse 2b automotive electrical disturbance in the ISO 7637-2 standard can be easily generated based on the mathematical expression for a double exponential waveform. It just a matter of understanding  the relation between the test pulse’s rise and duration times, and the double exponential waveform expression’s time constants, as we have shown here!

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