IEEE Circuits and Systems Magazine - Q3 2021 - 91

concepts of gain and phase margin derived from his now
famous plots. The method is based on the observation
that a log-representation of the magnitude (in dB) is additive
in the contributions of elementary factors of poles
and zeros in the transfer function, and the observation
that the instability of a fed-back system is generated
by positive feedback (i.e., a phase difference of 180 degrees
or more at some critical frequencies), an estimate,
which is obtained by comparing the magnitude plot with
the corresponding phase plot. Although the method has
good engineering properties and is very useful for the
initial design of a (linear time-invariant) system (like an
amplifier), it suffers from a lack of generality (the Bode
plots can only be derived fairly accurately for simple
systems), it does allow for quick and easy assessment
and provides a sometimes surprisingly accurate estimate
of stability. Bode had a good working relationship
with Harry Nyquist, who succeeded in deriving an exact
criterion for the stability of a system based on its (complex)
frequency response, drawn out in the complex
plane, and using complex function calculus.
But he made perhaps his most important contributions
at the onset of Second World War, with the development
of a fully automatic anti-rocket defense system.
It was a sophisticated example of Artificial Intelligence
avant la lettre. To develop it, Bode had to solve intricate
mathematical, communication, and control problems.
The input part of the system consists of the analysis of
radar images (also the radar was a new invention at the
time), locking the radar on the incoming rocket, calculating
as well as possible the rocket's trajectory from the
collected radar images, determining the required battery
settings, representing, and communicating this information
to the ground stations, which could then operate automatically
and in split seconds. For all these tasks some
nasty mathematical problems had to be solved, like the
inaccuracy of taking derivatives (estimating the speed
of the rocket), or the automatic implementation of mathematical
functions (there were no usable digital computers
yet). The system successfully defended London from
the V-1 flying bombs during Second World War. After the
war, Bode along with his wartime rival Werner von Braun
developer V-1 flying bomb, and, later, the father of the US
space program, served as members of the National Advisory
Committee for Aeronautics (NACA), the predecessor
of NASA. During the Cold War, he contributed to the
design and control of missiles and anti-ballistic missiles.
He made important contributions to the design, guidance
and control of anti-aircraft systems during Second
World War. He helped develop automatic anti-aircraft
control systems, whereby radar information was used
to provide data about the location of the enemy aircraft,
which was then fed back to the anti-aircraft artillery
THIRD QUARTER 2021
servomechanisms enabling automatic, radar-augmented
enemy aircraft ballistic tracking. The radar signal was
locked on target and its data was wirelessly transmitted
to a ground receiver that was connected to the artillery
servomechanism feedback control system, causing
the servo to accurately modify its angular position and
maintain it for an optimum amount of time, long enough
to fire at the calculated (predicted) coordinates of the
target and thus successfully track the target. The system
successfully defended London from the V-1 flying bombs
during Second World War. After the war, Bode along
with his wartime rival Werner von Braun developer of
the V-1 flying bomb, and, later, the father of the US space
program, served as members of the National Advisory
Committee for Aeronautics (NACA), the predecessor of
NASA. During the Cold War, he contributed to the design
and control of missiles and anti-ballistic missiles.
In 1944, Bode was placed in charge of the Mathematical
Research Group at Bell Labs, His work on electronic
communications, especially on filter and equalizer design,
continued during this time. In 1945 it culminated in
the publication of his book Network Analysis and Feedback
Amplifier Design (Van Nostrand Reinhold 1945),
which is considered a classic in the field of electronic telecommunications
and was extensively used as a textbook
for many graduate programs at various universities as
well as for internal training courses at Bell Labs. In 1952,
he was promoted to the level of Director of Mathematical
Research at Bell Labs. In 1955, he became Director of Research
in the Physical Sciences, and remained there until
1958, when he was promoted again to become one of the
two Vice Presidents in charge of Military Development
and Systems Engineering, a position he held up to his retirement.
He also became a director of Bellcomm Inc., a
company associated with the Apollo program. Bode was
in many ways a precursor of the modern methods in estimation
and control, which necessarily had to go back to
the time domain (as most of the systems used were now
time variant), but his work on these two fields (estimation
and control) provided for much problem setting and
direction. These now essential topics were then further
developed by Bellman and Kalman for use in the Apollo
program, and have become mainstays.
By the time of his retirement in October 1967, he held a
total of 25 patents in various areas of electrical and communications
engineering, including signal amplifiers and
artillery control systems. Soon after retirement, Bode
was elected to the academically prestigious Gordon McKay
Professor of Systems Engineering position at Harvard
University. During his tenure there, he pursued research
on military decision making algorithms and optimization
techniques based on stochastic processes, that
today play an essential role in modern estimation and
IEEE CIRCUITS AND SYSTEMS MAGAZINE
91
IEEE Circuits and Systems Magazine - Q3 2021

Table of Contents for the Digital Edition of IEEE Circuits and Systems Magazine - Q3 2021
