Overview

• A set of phase modulation sidebands are imposed to the main laser beam for control of the mode cleaner cavity and the main interferometer. The frequency of the sidebands are determined from the signal extraction and control scheme: 11MHz, 23.5MHz, and 55MHz.
• We are investigating a multiply resonant circuit to be attached to EOM in order to create those three pairs of sidebands with a single crystal.
• (What is motivation? Why single crystal? Why three eoms are not enough? Why triple electrode EOM is not enough?)

• The feasibility and the basic ideas of the triple resonant circuit was investigated by Stephanie Erickson, a 40m SURF student in 2009 Summer. Link to Stephanie's descriptions (What did she demonstrated?)

Steps for Development

• studying the principle of LC circuit + transformer

• investigation of loss effect in LC circuit

• make a test circuit (single resonant) with highest impedance ( - Dec.20)
• make a new transformer for matching the impedance of the test circuit ( - Dec. 25)
• performance test by using optical spectrum analyzer ( - Dec. 31)
• study of triple resonant circuit (- Jan.5)
• investigation of loss effect in the multi-resonant circuit ( - Jan.12)
• make a prototype circuit with highest impedance ( - Jan.13)
• make a new transformer for prototype ( - Jan. 20)
• performance test of prototype by optical analyzer ( - Jan. 25)
• final design and ordering (- Jan.31)
• performance test with ordered circuit
• installation

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1. Conceptual design

• The goal of this development is to make a triple-resonant circuit that operates an EOM. And we should make a high gain circuit to achieve sufficient amount of modulation depth. The conceptual design has been investigated by Stephanie.

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2. Fundamentals

• In this chapter the fundamentals of resonant circuit are explained.

2.1 Transformer

• The reason why we use a transformer are mainly follower;

  • handling high voltage, step up the voltage and impedance matching.

2.1.1 handling high voltage

• Our EOM has the modulation efficiency of ~13mrad/V and the desired modulation depth is typically 0.1-1rad. Therefore the voltage inputted to the EOM will reach 10-100V. In such high voltage regime the ordinary op-amplifiers are no longer works because those output voltage are limited to about +/- 15V which corresponds to the source voltage of the amplifiers. In contrast transformers are even available in such high voltage regime because the they works passively.

2.1.2 step-up gain and impedance matching

• For the transformer the gain is equal to its turn ratio. Hereafter We denote the turn ratio as n. Therefore in order to make a high gain resonant circuit, big number of turn ratio is required.

• However there is a limitation for the maximum turn ratio n_max. This limit comes from the impedance matching issue. Now consider the simple case like figure.1, a transformer with load impedance Z_L.

• The figure shows the equivalent circuit of transformer.

2.2 resonance with LC

• Basically the circuit is composed by only L and C. Inductance L has a angle of 90 deg from real axis, and Capacitor C has a angle of -90 deg from real axis in terms of impedance. In addition their amplitude in real-imaginary plane grow up along with frequency.

2.3 Loss

• In the ideal case, where no losses, we can get an infinite impedance. But in the real circuit

the impedance must be limited. The one of the component which makes impedance lower is losses.

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3. Study of Single resonant circuit

• In order to understand how the circuit works and how losses affects, we started with a single resonant circuit. The circuit is composed by L, C and transformer in parallel.

3.1 resonant impedance

• According to our measurement....

3.2 loss effect

• The loss effect has been directly observed via the impedance measurement.

3.3 design single-resonant circuit

• Based on the result described above, the single-resonant circuit is designed.

3.4 optical test

• So far we only think about electrical aspect, here the optical aspect is considered. The motivation of optical test is

3.5 conclusion

• Through whole measurement there are some suggestion for designing better circuit.

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4. multiply resonant circuit

4.1 what's difference from single-resonance ?

• Here we consider the difference between multi-resonant and single-resonant. This

4.2 design

• The requirements for the multiply-resonant circuit are follower;

4.3 performance test

• Here we will report the resultant performance of the circuit both in electrical and optical test.
• As we expected....

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App. impedance measurement

• In this chapter the technique for measuring the impedance by using Network Analyzer (Agilent AG4395A) is explained. The point is to reduce the reflective waves.