Poster by Dereje Worku (Research Experiences for Undergraduates, Center for Integrating Research and Learning, 2006 Class)

1
Frequency Drift with Temperature in a Tunnel
Diode Oscillator (TDO) Dereje G. Worku1, José
Medina2, Shalton Evans3 1Depertment of chemical
engineering and engineering physics N.C AT state
university. 2 Department of electrical
engineering, Universidad Del Turabo, Gurabo,
P.R. 3Department of chemistry and physics, School
of natural sciences environmental studies and
technology, Bahamas

Florida State University, NHMFL
REU 2006.
Abstract. In this experiment, its shown how
frequency drifts with temperature in a tunnel
diode oscillator. The main objective is to
measure the changes with temperature of each
component of an LC circuit and then to estimate
the frequency drift with temperature of a Tunnel
Diode Oscillator (TDO). Network Analyzer, Time
Domain Reflectometer (TDR), and a capacitance
bridge were used. We found that the TDO is
sensitive to extremely small changes in both
inductance and capacitance, but we were able to
estimate the frequency change from room
temperature (300 K) to liquid N2 (77 K) within
less than 5.
Figure 3. TDO, Frequency (Hz) vs.
time (s) as temperature decreases from room
temperature (300K) to liquid nitrogen temperature
(77K). Signal Freq_22pF_004 is less noisier.
Frequency drift657.4KHz
Table showing calculated values of inductance
of the coil, resistance of thermometer and
temperature (K)

Introduction The precision with which
frequencies can be measured has made the use of
oscillators ideal for experimental physics
studies.. Oscillators are widely utilized to
study material properties, such as magnetic
susceptibility, superconductivity, surface
impedance, thermal expansion, resistance,
capacitance and inductance. The instruments used
in this particular experiment are Tunnel Diode
Oscillator its an LC-tank resonator driven by a
tunnel diode. Mathematically the frequency,
inductance (L), and capacitance (C) are related
by the equation

Time Domain Reflectometer TDR works in
such a way that the step generator produces a
positive-going incident wave through a coax cable
at a velocity of propagation of the cable where
our device under test (coil) is attached at the
opposite end. As the pulse signal reaches our
sample part of it will be reflected back, and
displayed on the oscilloscope unfolding the
material property of the coil, almost
independently of the length and type of
transmission line.
Figure 2. The TDR set up The
Net Work Analyzer In this case a signal
generator produces a sinusoidal signal whose
frequency passes through a transmission line and
the devise under test to stimulate it. The
network analyzer measures the transmitted and
reflected signals from the device under
test. Experiments and Set up Parameters, and
methodologies considered in designing an LC
circuit to get a less noisy signal putting
capacitors and resistors of different magnitudes,
using shielding, grounding,
changing bias voltage, and avoiding any external
disturbance is the way to approach the targeted
result. For this particular experiment we used a
5-turn 2mm copper coil.

Figure 7. Inductance (H) of the coil vs
R_thermo (O)
Figure 4. Capacitance (pF) vs.
Resistance (O) of the thermometer. The 50O
resistance represents temperature of 300K and
107.79O represents a temperature of 77.
Figure 1. General TDO circuit diagram
Figure 8. Shows the frequency (Hz) of the
circuit containing the coil vs R_thermo (O) with
out the capacitor. Mixer frequency512.5MHz.
Figure 5. TDR, shows a snap shot of
38 signals voltage (v) vs. time (s) of the
circuit containing the coil with out the 22pF
capacitor. as temperature goes down.
Where R is the resistance of the coil ,dV is
the change in voltage, Vi is the initial voltage,
and 50O
Conclusion From the values obtained from
figures, 4, 7, and 8 the frequency drift as
temperature goes from room to liquid nitrogen
temperature is 684KHz, which is larger by 26.6KHz
from the frequency drift obtained in figure 3.
Some of the sources of the extra 26.6 KHz
frequency drift considered in this experiment
are I. Capacitance and inductance added by other
components of the circuit such as the copper
groundings, and signal carrier. II. Even so the
property of the coil and diode combined
capacitance is known, how the capacitance of the
diode behaves by itself with temperature is
unidentified.

Where inv is the exponent of the
exponential fitting curve.




Figure 6. The first top
signal from figure 5.

Acknowledgments I would like to extend my
appreciation to Dr.Kataline Martin, Dr.Stanley
Tozer, Dr Eric Palm, Kenneth Purcell, Jose
Sanchez, NHMFL, CIRL NSF, NC AT State
University, and all REU 2006 crews.
References Van Degrift Craig T. Tunnel Diode
Oscillator for 0.001 ppm measurements at low
Temperature (1974). Re. Sci. Instru., Vol. 46,
No. 5 May 1975 Dolocan Volcu. Determination of
material properties by using the reflection pulse
method (1994). Re. Sci. Instru. 65 (11),
November, 1994 Hewlett Packard application note
1304-2. Time Domain Reflectometry Theory