FIGURE 2. Hewlett-Packard Type 8405A:
Vector Voltmeter Pulse Generator,
showing modification for lower ground
impedance (green wires) which restored
the instrument to working condition.
duced on a circuit board in a shielded
cage with sliding ground clips on the
sides to contact the copper-clad circuit
board. There were also ground wires
on the edge connector. Producing a
signal at such frequencies — and with
such very precise and critical frequency
and phase control — requires a very
good ground. I suspected that the
ground connections to the circuit board
had somehow deteriorated over time.
Assuming 10 nh/cm (nanohenries
per centimeter) of wire length, and
four wires of about 2 cm length in
parallel, the inductance would
be about 5 nh and, at 3 GHz, the
inductive reactance is about 90 ohms.
What the reactance of the slide clips
was, I couldn’t possibly guess.
After making measurements,
testing, viewing waveforms, replacing
parts, making theological and biological comments in four letters, scratching
my head and almost making a hole,
somehow I decided to add some more
ground wires to the pulse generator
edge connector. They are the green
wires in Figure 2. It worked perfectly!
I can only assume that, over the
years, the circuit board grounding
slide clips corroded, the ground
impedance rose, which caused the
APC to fail. The extra ground wires
were each in parallel with the existing
ground circuit, lowering the ground
impedance and reducing interaction
with other circuits. That’s what can
happen when a wire acts like an
inductor and a resistor! NV
(1) B. Whitfield Griffith, Jr.
Radio-Electronic Transmission Fundamentals,
2000, ISBN 1-884932-13-4. Available
from the Amateur Radio Relay
League, www.arrl.org/qex/. ARRL
Order Number: RETF; $75 plus
shipping and handling. Order toll-free:
1-888-277-5289 or QUICK ORDER online.
( 2) Dr. F. E. Terman, Radio Engineer’s
Handbook, First Edition: 1943, Section
2: “Circuit Elements,” pp. 26-53.
McGraw-Hill Book Company.
( 3) Other books by Dr. Terman:
Electronic and Radio Engineering, 1955
Fundamentals of Radio, 1938
Electronic Measurements, 1952
If you can find these books
anywhere, and can afford them, grab
them; you’ll never regret it.
These books are worth any couple
dozen others that I can think of. Dr.
Terman was a great teacher; perhaps
the greatest electronics teacher ever.
The Griffith text guided me through an
AM broadcast transmitter installation.
I cannot recommend these books
You can see the current waveform leading the voltage waveform in a capacitive
reactance with a simple setup:
(1) The parts required are a 0.1 μF
capacitor and a 1.0 Ω resistor. The values
can be approximate.
( 2) Connect the capacitor and resistor
( 3) Connect a signal generator output to
the capacitor free end and ground to the
resistor free end. The generator should
be able to provide about 1.5V RMS at 30
kHz into a 50 Ω load.
( 4) Connect a dual-trace ‘scope so that
the generator output can be seen on
Channel 1, and the voltage across the 1.0
Ω resistor on Channel 2.
( 5) Adjust the scope’s vertical sensitivity
so that both traces cover the graticule
SEEING IS BELIEVING
( 6) Adjust the scope’s horizontal sweep
so that both traces show about one cycle
and, with the generator output turned
off, the traces are on the center horizontal line of the graticule. If there is DC in
the generator output (the Channel 1
trace moves vertically as you adjust the
generator output), switch the ‘scope
inputs to “AC coupling.”
( 7) You will see the Channel 2 trace is
to the left (leading) of the Channel 1
trace by about one-quarter of a cycle,
or about 90°.
The Channel 2 trace from the 1Ω
resistor is showing the current waveform
through the capacitor. The capacitive
reactance of the capacitor at 30 kHz is
about 50 ohms, so the 1Ω resistor, being
so much smaller, does not change the
phase relationship significantly.
If the capacitor were replaced by an
inductor of about 265 μH (inductive
reactance of about 50 ohms at 30 kHz),
the Channel 2 trace (current) would be to
the right (lagging) of the Channel 1 trace
by about a quarter of a cycle.
This is a hard concept: voltage and
current in phase in a resistance, current
leading the voltage by 90° in a capacitance, and current lagging the voltage by
90° in an inductance. It is the convention
to refer phase shift to the voltage
waveform, that is, the voltage waveform
is considered to be at 0°. Then, if the
current is ahead of the voltage (leading),
it is considered to be at a positive angle;
if the current waveform is behind
the voltage waveform (lagging) it is
considered to be at a negative angle.
I have found it easier, in a series
circuit, to think of the current waveform
as a reference, and then to think of the
voltage waveform as a result of the
effect of the resistance or reactance (or
combination) on the current. But then,
before any calculations, it is necessary to
readjust the observation to conform with
the convention (voltage at 0°).
February 2008 59