It comes as something of a surprise to most engineers that the –48V power distributed on a backplane exhibits a decidedly inductive impedance. Considering bypass capacitors are often excluded from the backplane, coupled with the lengthy path back to the –48V battery or power supply source, it seems unavoidable. The consequences of an inductive driving point impedance are twofold: first, for reasons entirely cosmetic, the ringing associated with insertion and other transient events are undesirable. Second, input reaction to high dI/dt conditions presents correspondingly high input voltage surges, placing the Hot Swap MOSFET as well as the operation of the Hot Swap controller at risk.

To mitigate these effects a network
comprising a clamping element in
parallel with a snubber is often found
in successful circuit implementations,
as seen in Figure 1. D3 serves to
clamp input reaction and the R8-C8
snubber eliminates ringing^{1}. Figure 2
shows the before-and-after results of
adding clamping and snubbing, under
conditions of insertion and circuit
breaker action.

Before

Without a clamp and a snubber,
MOSFET Q1’s drain-source capacitance
C_{OSS} resonates with little loss
against the inductance of the –48V
backplane distribution bus. The presence
of Schottky diodes D1 and D2
complicate matters, but at best the
diode in line with the lowest magnitude
input voltage adds capacitance
in parallel with C_{OSS}, and at worst the
active diode peak detects the input
ring, storing the energy (and high voltage)
on C_{OSS}. Because C_{OSS} exhibits a
strong voltage dependency, the peak
ring voltage at insertion can avalanche
the MOSFET or the LT4250. The 200V
transient input rating of the LTC1921
generally keeps it out of harm’s way.
The energy available at the peak voltage
is limited, and rarely is the source
of destruction.

If the circuit breaker function of
the LT4250 is invoked by a sustained
overload, the inductance of the –48V
wiring is loaded with ½Li^{2}, which
represents a potentially destructive
energy. The energy is high enough to
drive something, usually the MOSFET,
into avalanche as shown by the flattened
portion of the waveform. Once
the input current drops to zero, the
remaining energy rings off in a manner
not dissimilar to the insertion phase
of operation.

After

The addition of a clamping diode and R-C snubber eliminates the aforementioned high voltage transients. At insertion, ringing is eliminated and overshoot controlled by the R8-C8 snubber of Figure 1. Input reaction during a circuit breaker event is clamped to a safe level by D3, a transient suppression diode. Subsequent ring-off and attendant noise burst is again controlled by the snubber.

To quantify the stored energy and to optimally size the snubber and clamping components, one must know something about the magnitude of inductance in the –48V feed. Measuring this impedance is problematic, given the risk inherent in connecting a sensitive, costly piece of test equipment such as an HP4815A to a multi-kW –48V supply bus. Fortunately there is an easier risk-free way to get the required information, using a simple oscillator circuit where the unknown inductance resonates with a known capacitance. In all but extreme cases this method gives results adequate for quantifying the inductance of the –48V feed.

Simple Test Oscillator

Figure 3 shows a test circuit that, with
the aid of a frequency meter^{2}, can measure
the inductance of the –48V supply
line. The circuit is essentially a Colpitts
oscillator, where both the resonating
inductance and power are furnished
by the –48V bus. The capacitive arm
of the oscillator comprises C1 and C2,
with the tap at the junction of C1 and
C2 feeding the emitter of Q1. Coupling
is set to accommodate inductances
down to ≈100nH. Base components
provide bias and bypassing, while R3
and R4 establish an emitter current
of approximately 11mA, operating
the transistor in a region of favorable
frequency. Two resistors are utilized
in the emitter circuit to distribute dissipation
and permit use of common
quarter-watt units. A tiny, off-the-shelf
current transformer couples signal
to a 50Ω termination at a frequency
counter.

Measurements are made by plugging the test circuit into a –48V backplane, picking up –48V BATT and –48V RTN and measuring the oscillator frequency. The loop inductance between these two points together with the circuit capacitance determines the frequency of oscillation.

It is important to transformer couple the output signal so that the frequency counter is not grounded to –48V RTN. First, there is concern about DC ground loops since –48V RTN is not earth or chassis ground. Second, if the –48V RTN is contaminated with noise, it could contaminate the oscillator frequency measurement. Third, –48V RTN contributes its own share of inductance, and this would be disturbed by the introduction of the frequency counter’s ground at that point. Transformer coupling eliminates these issues.

Use

The oscillator circuit is most usefully constructed on a small circuit board complete with a backplane power connector and a BNC for frequency counter attachment. This assembly is then plugged into the backplane to measure the inductance of the –48V feed. Characterization of various slots and backplanes proceeds quickly as the test circuit is moved from one connector to the next and the frequency logged. The measured inductance varies widely depending on the presence of adjacent cards or noise filters, distance to the power source, backplane and bus bar construction and so on.

Inductance is calculated from the measured frequency of oscillation using the basic relation

where ω is the radian frequency of
oscillation and C_{O} is the oscillator’s
total equivalent capacitance at the
collector of Q1.

The capacitance C_{O} is roughly

For example, a measurement taken on the author’s test oscillator produced the following results (a rearrangement of equation (1)):

Note that for the purposes of designing
snubbers and selecting transient
clamps, a value of C_{O} = 1.8nF yields
acceptable results when calculating
L.

Calibration

Accumulated tolerances in oscillator
components, as well as the performance
of the transistor, affect the
value of C_{O} and therefore the accuracy
of the previous calculations. While
the approximate value of 1.8nF is
entirely adequate for snubber designs,
a potentially more exacting figure for
the “correlation” capacitance is easily
computed (without the need for a
standard inductor) using the following
method.

First, attach a 1µH to 10µH inductor
between the collector of Q1 and a –48V bench supply (see Figure 4). To
eliminate erradic readings caused by
test lead inductance, bypass the –48V
supply at the inductor. Measure the
resulting frequency, f1. Now add a
capacitor C_{X} of 1nF to 4.7nF to Q1’s collector
and measure the new frequency,
f_{2}. The two operating conditions are
related by manipulating equation (1)
to eliminate inductance. Thus

The author’s setup measured f1 =
2.9376MHz and f_{2} = 1.5663MHz (C_{X}
= 4.7nF); from equation (5) C_{O} was
apparently 1.866nF, or about 3.5%
higher than calculated from equation
(2) and the components’ marked
values.

This calibration method is independent
of the test inductor, but limited
by the accuracy of the extra capacitor,
C_{X}. A 5% silver mica unit is sufficient
to give verification of equation (2). This
figure improves if C_{X} is first measured
with an accurate capacitance meter to
establish a more exacting value.

Calibration for Advanced Users

A series of measurements made with
several C_{X} calibration “standards” can
help statistically improve the accuracy
of C_{O}, or at least increase the user’s
faith in the perceived value. Again no
“standard” inductor is necessary, only
a fixed unit that doesn’t change value
between readings.

A series of such measurements
taken by the author are shown in
Table 1, and the data are plotted in Figure
5. It is easy to see the straight-line
relationship between total oscillator
capacitance (C_{O} + C_{X}) and 1/ω^{2}, and
it is that relationship which allows
us to graphically deduce C_{O} from the
x-axis intercept.

C_{X} (nF) |
f (MHz) | 1/ω^{2} (Radians–^{2}) |

0 | 2.9376 | 2.9353 • 10^{–15} |

1 | 2.4004 | 4.3962 • 10^{–15} |

2.2 | 2.0132 | 6.2498 • 10^{–15} |

3.3 | 1.7742 | 8.0470 • 10^{–15} |

4.7 | 1.5663 | 10.325 • 10^{–15} |

In this case there is fair graphical agreement with the values calculated from equations (2) and (5), as the line appears to cross zero at ≈1.8nF. A curve-fitting utility in the graphing program predicted an intercept of 1.813nF.

This method is really just an extension of the calculation made in equation (5); it’s just that equation (5) was a 2-point approximation, while here we have extended it to 5 points.

Measuring Inductance and Capacitance

A second purpose for plotting oscillator
capacitance against 1/ω^{2} is that it
also resolves distributed capacitance
inherent in the backplane and wiring
harness.

Using the method of Table 1 and
Figure 5 as a starting point, suppose
the oscillator is now connected to a
backplane and the same sequence of
measurements made as C_{X} varies. To
facilitate measurements, several C_{X}
capacitors are mounted on the test
oscillator card and selected with a
switch or jumpers. A new set of data
as plotted in Figure 6 results.

Again, with the aid of a straight
edge or curve-fitting utility, the x-axis
intercept is found to be 3.081nF. This
value is the sum of the oscillator’s
built-in capacitance C_{O}, plus the
capacitance contributed by the backplane
and wiring harness. Removing
C_{O}, we find that

Note that the inductance calculation
uses the frequency value found at
C_{X} = 0, but uses the projected capacitance
of 3.081nF at 1/ω^{2} = 0.

Snubber Design

For Hot Swap controller circuits such as shown in Figure 1, it is well to size the snubbing capacitance C8 to be 10 times all other circuit capacitances combined. In Figure 1, capacitance is contributed by circuit board traces (small, usually neglected), D3 (400pF), and perhaps one of the input diodes (100pF in D2, for example). The largest contributor is Q1, weighing in at 1500pF under zero bias, and 250pF at 50V. Assuming 500pF as the effective value, the total capacitance to be snubbed in Figure 1 is approximately 1nF, leading us to a value of 10nF for the snubbing capacitor. If we include the backplane capacitance measured in Figure 6, a value of 10 • 2.268nF or ≈22nF is adequate.

The snubbing resistor R8 is sized so that the circuit Q is a conservative 0.1 and the effects of circuit capacitance are nullified. Q is given by the equation

Setting Q = 0.1 and rearranging equation (6) for our special case with C8 = 22nF and L = 1.6µH gives

This is where our measurement
of “L” comes in handy—to compute
the damping necessary to control Q.
With standard values of R8 = 82Ω
and C8 = 22nF, ringing is eliminated and overshoot is limited to less than
100V_{PK} during initial insertion on a
48V supply.

Nevertheless, R8 and C8 have different values in Figure 1. C8 has been increased in value to serve as a hold up capacitor in the event the input supply collapses, thereby guaranteeing operation of the LT4250 circuit breaker and MOSFET shut-off. The operating Q of C8 and R8 in Figure 1 is ≈0.04.

Input Clamp, D3

Again referring to Figure 1, D3 is sized to handle the energy stored in the backplane and wiring harness inductance. Sticking with 1.6µH, suppose the peak input current reached 50A during a zero-ohm failure of C3. The energy stored in the –48V input inductance is given by

Examination of the SMAT70A data sheet reveals that this device handles in excess of 200mJ; thus it is adequate for this application.

The presence of distributed capacitance on the backplane and in the –48V wiring harness plays an interesting role. First, the snubber must be oversized to account for the hindrance of this extra capacitance as we saw in earlier calculations (equation (7)). Second, the distributed capacitance helps the clamp D3 by absorbing some of the inductive energy, although 1.268nF absorbs less than 5µJ in this example. From this we can conclude that any distributed “parasitic” capacitance affects the snubber design long before there is any need to account for it in the selection of a clamp.

Conclusion

The test oscillator described here is suitable for measuring backplane and wiring harness inductance in –48V systems in the range of 100nH to 100µH or more. Parasitic capacitance can be measured as well, over a range of less than 100pF to 5nF or more. If the circuit refuses to oscillate you can assume that either the inductance is well damped, or it is shunted by large value capacitances.

**Notes**

- This subject is treated in some detail in the LTC1647 data sheet, Figures 9, 10, and 11 inclusive.
- An hp 5210A Frequency Meter or any common counter gives adequate accuracy for most measurements.