The MCL1-540 comes with different input module options, MCL1M-112-1.8, MCL1M-112-2.0, MCL1M-112-4 and MCL1M-112-18. This note focuses on the difference between the different options.

## Background

The input noise, input impedance, input bias- and input offset current are depending on each other, and when selecting the right input option, the most critical parameter needs to be identified depending on the application. In general, a low input noise density comes along with a low input impedance and high input bias current while low input offset/bias currents and a high input impedance is accompanied by a higher input noise density.

The following table gives an overview of the typical parameters.

Module | Input noise | Input impedance | Input bias current | Input offset current | Noise equivalent resistance | High-gain bandwidth |
---|---|---|---|---|---|---|

MCL1M-112-1.8 | 1.8 nV/√Hz / 1.5 pA/√Hz | ~1 GΩ | 50 nA | 0.5 nA | ~200 Ω | 100 kHz |

MCL1M-112-2.0 | 2.0 nV/√Hz / 1.2 pA/√Hz | ~1 GΩ | 5 nA | 0.5 nA | ~200 Ω | 100 kHz |

MCL1M-112-4 | 4 nV/√Hz / 200 fA/√Hz | ~30 GΩ | 0.1 nA | 0.1 nA | ~1 kΩ | 100 kHz |

MCL1M-112-18 | 18 nV/√Hz / 1 fA/√Hz | ~1 TΩ | 10 pA | 0.6 pA | ~20 kΩ | 10 kHz |

In most cases, the input bias/offset currents are more crucial for an experimental setup than the input impedance. Furthermore, effects of the cable and experimental setup like stray capacitance, creepage and leakage are especially for the MCL1M-112-18 more critical than the amplifiers input impedance. The MCL1M-112-18 is only recommended when measurements are conducted at a frequencies well below 10 kHz.

## Thermal noise

Thermal (Johnson/Nyquist) noise is arising from any resistor due to thermal fluctuation of the charge carriers. Connecting a resistor, probe or sample having a source resistance *R* to the amplifier input will result in an additional noise besides the amplifiers own input noise. At a given temperature *T*, thermal noise density *v*_{n} specified in V/√Hz is given by* v*_{n} = √(4*k*_{B}*TR*),

where *k*_{B} is the Boltzmann constant. Therefore, for high source resistances, the noise floor is not dominated by the input amplifier noise but the source resistance, and a lower amplifier noise does not improve the measurement result. The above table lists the source resistance where the thermal noise is similar to the different modules noise floor.

## Input bias / offset current

Due to the non-ideal behavior of amplifiers, a small leakage current is always flowing through all inputs of an amplifier. This current is called input bias current, while the difference in current between the two inputs is called input offset current. These currents are dependent on both temperature and common mode voltage, and can differ between different amplifiers. The most noticeable side effects can be self-heating of the sample and a DC offset. The lock-in signal itself is usually not affected by these currents.

## Input Impedance / capacitance

At higher frequencies, cable capacitance can have a strong effect on the measurement results. Coaxial cables and Ethernet cables typically have a capacitance in the order of 50 pF per Meter*,* resulting in a cable impedance of *X*_{C} = 1/(2π*fC*). Normally, effects from cable capacitance are much larger then the amplifiers own input capacitance and input impedance.

## Dynamic Reserve

The dynamic reserve is the maximum ratio between the smallest detectable signal and a disturbing signal at a different frequency.

Range | MCL1M-112-1.8 | MCL1M-112-4 | MCL1M-112-18 |
---|---|---|---|

10 V | >140 dB | >140 dB | >140 dB |

5 V | |||

2 V | |||

1 V | |||

500 mV | |||

250 mV | |||

10 0mV | |||

50 mV | |||

20 mV | |||

10 mV | |||

4 mV | |||

2 mV | 120 dB | 113 dB | 100 dB |

## Summary

Application | MCL1M-112-1.8/2.0 | MCL1M-112-4 | MCL1M-112-18 |
---|---|---|---|

Superconductors | ++ | + | – |

Semiconductors | + | ++ | – |

Thermometers | — | 0 | ++ |