# A Numerical Treatment of the Rf SQUID: II. Noise Temperature

## Abstract

We investigate rf SQUIDs (Superconducting QUantum Interference Devices), coupled to a resonant input circuit, a readout tank circuit and a preamplifier, by numerically solving the corresponding Langevin equations and optimizing model parameters with respect to noise temperature. We also give approximate analytic solutions for the noise temperature, which we reduce to parameters of the SQUID and the tank circuit in the absence of the input circuit. The analytic solutions agree with numerical simulations of the full circuit to within 10%, and are similar to expressions used to calculate the noise temperature of dc SQUIDs. The best device performance is obtained when {beta}{sub L}{prime} {triple_bond} 2{pi}LI{sub 0}/{Phi}{sub 0} is 0.6-0.8; L is the SQUID inductance, I{sub 0} the junction critical current and F{sub 0} the flux quantum. For a tuned input circuit we find an optimal noise temperature T{sub N,opt} {approx} 3Tf/f{sub c}, where T, f and f{sub c} denote temperature, signal frequency and junction characteristic frequency, respectively. This value is only a factor of 2 larger than the optimal noise temperatures obtained by approximate analytic theories carried out previously in the limit {beta}{sub L}{prime} << 1. We study the dependence of the noise temperature on various model parameters, and givemore »

- Authors:

- Publication Date:

- Research Org.:
- COLLABORATION - U.Tubingen/Germany

- OSTI Identifier:
- 928721

- Report Number(s):
- LBNL-62298-(II)

Journal ID: ISSN 0022-2291; JLTPAC; R&D Project: 504801; BnR: KC0202020; TRN: US0803251

- DOE Contract Number:
- DE-AC02-05CH11231

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Low Temperature Physics; Journal Volume: 149; Journal Issue: 5-6; Related Information: Journal Publication Date: 12/2007

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75; CRITICAL CURRENT; INDUCTANCE; LANGEVIN EQUATION; PERFORMANCE; TANK CIRCUITS

### Citation Formats

```
Kleiner, Reinhold, Koelle, Dieter, and Clarke, John.
```*A Numerical Treatment of the Rf SQUID: II. Noise Temperature*. United States: N. p., 2007.
Web. doi:10.1007/s10909-007-9512-9.

```
Kleiner, Reinhold, Koelle, Dieter, & Clarke, John.
```*A Numerical Treatment of the Rf SQUID: II. Noise Temperature*. United States. doi:10.1007/s10909-007-9512-9.

```
Kleiner, Reinhold, Koelle, Dieter, and Clarke, John. Mon .
"A Numerical Treatment of the Rf SQUID: II. Noise Temperature". United States.
doi:10.1007/s10909-007-9512-9. https://www.osti.gov/servlets/purl/928721.
```

```
@article{osti_928721,
```

title = {A Numerical Treatment of the Rf SQUID: II. Noise Temperature},

author = {Kleiner, Reinhold and Koelle, Dieter and Clarke, John},

abstractNote = {We investigate rf SQUIDs (Superconducting QUantum Interference Devices), coupled to a resonant input circuit, a readout tank circuit and a preamplifier, by numerically solving the corresponding Langevin equations and optimizing model parameters with respect to noise temperature. We also give approximate analytic solutions for the noise temperature, which we reduce to parameters of the SQUID and the tank circuit in the absence of the input circuit. The analytic solutions agree with numerical simulations of the full circuit to within 10%, and are similar to expressions used to calculate the noise temperature of dc SQUIDs. The best device performance is obtained when {beta}{sub L}{prime} {triple_bond} 2{pi}LI{sub 0}/{Phi}{sub 0} is 0.6-0.8; L is the SQUID inductance, I{sub 0} the junction critical current and F{sub 0} the flux quantum. For a tuned input circuit we find an optimal noise temperature T{sub N,opt} {approx} 3Tf/f{sub c}, where T, f and f{sub c} denote temperature, signal frequency and junction characteristic frequency, respectively. This value is only a factor of 2 larger than the optimal noise temperatures obtained by approximate analytic theories carried out previously in the limit {beta}{sub L}{prime} << 1. We study the dependence of the noise temperature on various model parameters, and give examples using realistic device parameters of the extent to which the intrinsic noise temperature can be realized experimentally.},

doi = {10.1007/s10909-007-9512-9},

journal = {Journal of Low Temperature Physics},

number = 5-6,

volume = 149,

place = {United States},

year = {Mon Jan 15 00:00:00 EST 2007},

month = {Mon Jan 15 00:00:00 EST 2007}

}