Thermal Noise Behavior of the Bridge Circuit
This paper considers a connection between the deterministic and noisy behavior of nonlinear networks. Specifically, a particular bridge circuit is examined which has two possibly nonlinear energy storage elements. By proper choice of the constitutive relations for the network elements, the determ...
| Autors principals: | , , |
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| Format: | Technical Report |
| Idioma: | English |
| Publicat: |
2005
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| Accés en línia: | http://hdl.handle.net/1721.1/7513 |
| _version_ | 1826203126003138560 |
|---|---|
| author | Coram, Geoffrey J. Anderson, Brian D.O. Wyatt, John L. |
| author_facet | Coram, Geoffrey J. Anderson, Brian D.O. Wyatt, John L. |
| author_sort | Coram, Geoffrey J. |
| collection | MIT |
| description | This paper considers a connection between the deterministic and noisy behavior
of nonlinear networks. Specifically, a particular bridge circuit is examined which has
two possibly nonlinear energy storage elements. By proper choice of the constitutive
relations for the network elements, the deterministic terminal behavior reduces to that
of a single linear resistor. This reduction of the deterministic terminal behavior, in
which a natural frequency of a linear circuit does not appear in the driving-point
impedance, has been shown in classical circuit theory books (e.g. [1, 2]). The paper
shows that, in addition to the reduction of the deterministic behavior, the thermal
noise at the terminals of the network, arising from the usual Nyquist-Johnson noise
model associated with each resistor in the network, is also exactly that of a single
linear resistor. While this result for the linear time-invariant (LTI) case is a direct
consequence of a well-known result for RLC circuits, the nonlinear result is novel. We
show that the terminal noise current is precisely that predicted by the Nyquist-Johnson
model for R if the driving voltage is zero or constant, but not if the driving voltage is
time-dependent or the inductor and capacitor are time-varying |
| first_indexed | 2024-09-23T12:32:04Z |
| format | Technical Report |
| id | mit-1721.1/7513 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T12:32:04Z |
| publishDate | 2005 |
| record_format | dspace |
| spelling | mit-1721.1/75132019-04-12T08:40:32Z Thermal Noise Behavior of the Bridge Circuit Coram, Geoffrey J. Anderson, Brian D.O. Wyatt, John L. This paper considers a connection between the deterministic and noisy behavior of nonlinear networks. Specifically, a particular bridge circuit is examined which has two possibly nonlinear energy storage elements. By proper choice of the constitutive relations for the network elements, the deterministic terminal behavior reduces to that of a single linear resistor. This reduction of the deterministic terminal behavior, in which a natural frequency of a linear circuit does not appear in the driving-point impedance, has been shown in classical circuit theory books (e.g. [1, 2]). The paper shows that, in addition to the reduction of the deterministic behavior, the thermal noise at the terminals of the network, arising from the usual Nyquist-Johnson noise model associated with each resistor in the network, is also exactly that of a single linear resistor. While this result for the linear time-invariant (LTI) case is a direct consequence of a well-known result for RLC circuits, the nonlinear result is novel. We show that the terminal noise current is precisely that predicted by the Nyquist-Johnson model for R if the driving voltage is zero or constant, but not if the driving voltage is time-dependent or the inductor and capacitor are time-varying Supported by the National Science Foundation under Grant 94-23221, by DARPA/ARO under Contract DAAH04-94-G-0342, and by the NEC Research Institute, Princeton, New Jersey. 2005-01-13T20:05:38Z 2005-01-13T20:05:38Z 2000-02-18 Technical Report http://hdl.handle.net/1721.1/7513 en Technical Report (Massachusetts Institute of Technology, Research Laboratory of Electronics);634 549484 bytes application/pdf application/pdf |
| spellingShingle | Coram, Geoffrey J. Anderson, Brian D.O. Wyatt, John L. Thermal Noise Behavior of the Bridge Circuit |
| title | Thermal Noise Behavior of the Bridge Circuit |
| title_full | Thermal Noise Behavior of the Bridge Circuit |
| title_fullStr | Thermal Noise Behavior of the Bridge Circuit |
| title_full_unstemmed | Thermal Noise Behavior of the Bridge Circuit |
| title_short | Thermal Noise Behavior of the Bridge Circuit |
| title_sort | thermal noise behavior of the bridge circuit |
| url | http://hdl.handle.net/1721.1/7513 |
| work_keys_str_mv | AT coramgeoffreyj thermalnoisebehaviorofthebridgecircuit AT andersonbriando thermalnoisebehaviorofthebridgecircuit AT wyattjohnl thermalnoisebehaviorofthebridgecircuit |