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.

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 piece-wise 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
exponential having different time constants, as shown in the expression:

*U*_{DE}
= U_{A}(e^{-K1t} – e^{-K2t})

Where U_{A} is the electrical system (alternator)
voltage, K_{1} is the slow time constant related to t_{d}, the
duration of the test pulse, and K_{2} is the fast time constant related
to t_{r}, 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 can be defined as:

*K*_{1}
= (2.303/t_{d}) *Where t*_{d} 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:

*K*_{2}
= (2.197/t_{r}) *Where t*_{r} is the rise time (for the 10% to 90%
transition)

The important thing here is that this is valid for when t_{d}
>> t_{r}. 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

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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