We investigate a simple variation of the series RLC circuit in which antiparallel diodes replace the resistor. The result is a damped harmonic oscillator with a nonlinear damping term that is a maximum at zero current and decreases inversely with the current for currents far from zero. Unlike the standard RLC circuit, the behavior of this circuit is amplitude dependent. The transient response makes a transition from underdamped to overdamped behavior, and the resonance response of the steady-state driven oscillator becomes sharper as the source amplitude increases. A set of nonlinear differential equations is derived for the circuit and integrated numerically for comparison with measurements. The equipment is inexpensive and common to upper level physics labs.

Topics
Nonlinear systems, RLC circuit, Electrical components, Electrical properties and parameters, Signal generators, Harmonic oscillator, Wave forms, Resistivity measurements, Ceramics, Education
1.
P. S.
 
Linsay
, “
Period doubling and chaotic behavior in a driven anharmonic oscillator
,”
Phys. Rev. Lett.
https://doi.org/10.1103/PhysRevLett.47.1349
 
47
,
1349
–
1352
(
1981
).
Google Scholar
Crossref
Search ADS
 
2.
J.
 
Testa
,
J.
 
Perez
, and
C.
 
Jeffries
, “
Evidence for universal chaotic behavior of a driven nonlinear oscillator
,”
Phys. Rev. Lett.
https://doi.org/10.1103/PhysRevLett.48.714
 
48
,
714
–
717
(
1982
).
Google Scholar
Crossref
Search ADS
 
3.
R. W.
 
Rollins
 and
E. R.
 
Hunt
, “
Exactly solvable model of a physical system exhibiting universal chaotic behavior
,”
Phys. Rev. Lett.
https://doi.org/10.1103/PhysRevLett.49.1295
 
49
,
1295
–
1298
(
1982
).
Google Scholar
Crossref
Search ADS
 
4.
R.
 
Van Buskirk
 and
C.
 
Jeffries
, “
Observation of chaotic dynamics of coupled nonlinear oscillators
,”
Phys. Rev. A
https://doi.org/10.1103/PhysRevA.31.3332
 
31
,
3332
–
3357
(
1985
).
Google Scholar
Crossref
Search ADS
 
5.
A.
 
Iobe
 and
Y.
 
Abe
, “
Experimental observation of indeterminate transition in a driven R-L-diode resonator
,”
Physica D
 
116
,
355
–
362
(
1998
).
Google Scholar
Crossref
Search ADS
 
6.
J.
 
Millman
 and
C. C.
 
Halkias
,
Electronic Devices and Circuits
(
McGraw-Hill
,
New York
,
1967
), pp.
124
–
129
.
Google Scholar
 
7.
M. H.
 
Jones
,
A Practical Introduction to Electronic Circuits
, 3rd ed. (
Cambridge U. P.
,
Cambridge
,
1995
), p.
125
.
Google Scholar
Crossref
Search ADS
 
8.
E. H.
 
Hellen
, “
Verifying the diode-capacitor circuit voltage decay
,”
Am. J. Phys.
https://doi.org/10.1119/1.1578070
 
71
,
797
–
800
(
2003
).
Google Scholar
Crossref
Search ADS
 
9.
I. J.
 
Bahl
,
Lumped Elements for RF and Microwave Circuits
(
Artech House
,
Norwood, MA
,
2003
), p.
170
.
Google Scholar
 
10.
J. C.
 
Sprott
, “
A new class of chaotic circuit
,”
Phys. Lett.
 
266
,
19
–
23
(
2000
).
Google Scholar
Crossref
Search ADS
 
11.
J. C.
 
Sprott
, “
Simple chaotic systems and circuits
,”
Am. J. Phys.
https://doi.org/10.1119/1.19538
 
68
,
758
–
763
(
2000
).
Google Scholar
Crossref
Search ADS
 
© 2007 American Association of Physics Teachers.
2007
American Association of Physics Teachers
AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.