TAMA coil driver modification
Gerhard Heinzel, TAMA Project, NAO Mitaka
April 14, 2000

1Introduction

The coil drivers are a crucial part of the TAMA interferometer. They are used tocontrol the position and orientation of the suspended mirrors. Both the longitudinal
and alignment control loops use them as their actuators. Low noise and high dynamic
range are very important. As with many such circuits, stability of the circuit is noteasy to obtain. The circuits were designed by K. Kawabe, who spent a long time inexperimentally making the circuits stable. Recently, however, it has been discoveredthat some of them oscillate at some MHz. Therefore a new stability analysis has been
done with LISO, the results of which are reported here.

2Coil impedance

Figure 1: Impedance model for a typical TAMA coil.

Figure 1 shows a model for the coil impedance including the typical cable (approx. 2 m long). It was obtained by first measuring the impedance with a RF network
analyzer, leading to the model without C4 and C5, and later refined as described below.
Figure 2 shows the measured data and fitted model, and Figure 3 shows the corresponding impedance of the coil.
As soon as an intermediate version of the coil driver circuit was built that wasstable enough to measure transfer functions, the measured transfer function was used10-5-1045

dB-20-250-30

Phase [Degree]-15-35-45-40-45-50
1000001e+06
Frequency [Hz]1e+07

U(n4) [V/V] dB
U(n4) [V/V] Phasetama/coil3.dat dBtama/coil3.dat Phase

Figure 2: Measured data and fitted model for the coil impedance measurement. (transferfunction with 50 Ohm source and load).

90100000

10000

Abs

10000100Phase [Degree]

45-45
1011000-90
10000

1000001e+06
Frequency [Hz]1e+07

Zin [Ohm] Phase

Zin [Ohm] Abs

Figure 3: Impedance of a typical TAMA coil as determined from the above model.

2to refine the model, in particular add capacitors C4 and C5.
Although the model is still not perfect, it was good enough for the calculations
described in this document.

3Coil driver circuit

Figure 4 shows the circuit of the coil driver. The circuit shown in Figure 4 with theFigure 4: Circuit diagram of the TAMA coil driver.

component values printed in small typeface is the old circuit used up to now, while thecomponent values printed in large typeface represent the new circuit (already installed).
It is essentially the standard voltage-to-current converter with the adjustable 50 Ωresistor R1 . . . R4 as scaling resistor. The additional 50 Ω resistor R7 does not change
the current-to-voltage transfer function. It doubles, however, the voltage drop at thereadout point X4 , making possible a readout of the coil current with slightly lower noise(see Section 6 below), at the expense of a reduced dynamic range.
The output current of the main op-amp (AD797) is boosted by the EL2099 Video
op-amp, which is used in the noninverting configuration. While the old circuit used theEL2099 with a voltage gain of 2, the new circuit uses it as voltage follower (gain = 1).
The 470 Ω feedback resistor R21/22 is still necessary, because the EL2099 is a currentfeedback amplifier.
There are two main stability problems in this circuit:3• Any voltage-to-current converter with an inductive load tends to have stabilityproblems. This is especially true if the load has resonances at frequencies where
the op-amps still have gain, as is the case here. The standard solution is to add aseries RC ’snubber’ circuit parallel to the load (R81 /C37 in Figure 4). The valuesof R and C can either be found experimentally, or by LISO (in complicated casessuch as this one, an iterative process involving both approaches works best).
• The AD797 tends to have stability problems in many circuits, even with lessproblematical loads. These problems are enhanced in the circuit discussed here,
because the current driver (EL2099) has a smaller bandwidth than the AD797,
meaning that additional phase delays are introduced at frequencies where theAD797 still has gain. In the old circuit, the voltage gain of the current buffer madethe situation even worse. The remedy is the lowpass-filter R15 /C3 /R17 , which
reduces the open-loop gain of the op-amp’s feedback loop at high frequencies.

4Old circuit

The circuit shown in Figure 4 with the component values printed in small typeface isthe old circuit which had been used up to now. Figure 5 shows its computed transferfunction, both with and without the additional 50 Ω resistor (this transfer function
could not be measured due to instability). The op-amp open-loop gain (Figure 6) has
stability problems near 400 kHz, where the transfer function has a high-Q peak, andalso at several frequencies between 1 MHz and 10 MHz.

5New circuit

After some calculation and experimentation the new circuit (shown in Figure 4 withthe component values printed in large typeface) was found.
The voltage gain of the current buffer was changed from 2 to 1 by removing R19 ,and the compensation components C3 , R81 and C37 were changed.
Figure 7 shows its computed and measured transfer functions. The computed transfer function represents input voltage −→ coil current, while the measured one represents
input voltage −→ voltage at readout point, the difference between the two being thescale factor (50 Ω) and the currewnt through the compensation network.
Figure 8 shows the computed op-amp open-loop gain (i.e. stability function) if theAD797 in this circuit, without the additional 50 Ω readout resistor. The unity-gain
frequency is 3 MHz, with a phase margin of 50◦ . Without the resistor, it is 52◦ at2 MHz. No oscillation was observed in the prototype of the new circuit, for any input
signal and any combination of short cables/long cables and 50 Ω readout resistor/no4

1001Phase [Degree]

0.1

Abs

0.01
0.001
0.0001
1e-05
1e-06
1e-07
10100

1000

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100000Frequency [Hz]

1e+06

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1e+08

I(lx) [A/V] Abs

U(n3) [V/V] Abs

Figure 5: Transfer function of the old TAMA coil driver, from the input to the voltage at theEL2099’s output (’n3’) and to the coil current (’lx’).

Op-amp stability ’coildrv/coildrvold’
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180

1401009080
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op1 dB

101001000 10000 100000 1e+06
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op2 phase

Figure 6: Open-loop gain of the old TAMA coil driver.

5

Phase [degrees]Open loop gain [dB]120

10135

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Abs

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1e-05

-135

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Frequency [Hz]

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I(lx) [A/V] Abs
I(lx) [A/V] Phase

coildrv/newtf0.dat Abs
coildrv/newtf0.dat Phase

Figure 7: Transfer function of the new TAMA coil driver without the additional 50 Ω readoutresistor. The curves starting at 10 kHz are measured transfer functions to the readout point,
while the curves starting at 10 Hz are simulated to show the current through the coil (i.e.
excluding the compensation network).

6

readout resistor. However, the stability is strongly dependent on the load, such thatany change in the cable or even the grounding of the cable screen might change thesituation and require a new analysis.

Op-amp stability ’coildrv/ctf’
160180140

10080906040

Phase [degrees]Open loop gain [dB]120

2000-201

op1 dB

10100

1000 10000 100000 1e+06
Frequency [Hz]op1 phase

op2 dB

1e+07

op2 phase

Figure 8: Open-loop gain of the AD797 op-amp in the new circuit.

6Noise and readout system

Since the coil driver described in this document acts directly on the suspended mirrors of
the interferometer, its noise is of utmost importance. Figure 9 shows the noise current√through the coil, referred to the input (and hence expressed as equivalent V/ Hz at theinput). The two main contributors are also plotted, voltage input noise of the AD797(dominant up to 3 kHz) and current input noise of the EL2099. The total noise at 1 kHz√
is 1.4 nV/ Hz, and it is dominated by the voltage noise of the AD797, a situation that
can hardly be improved. The noise level at the input of the coil driver will almost
always be much bigger than this.
√In future there may be situations where the 1.4 nV/ Hz added by the coil driverare a measurable contribution to the overall interferometer noise. If the open-loop
gain of the relevant longitudinal control loop (i.e. L− ) is still > 1 at measurement
frequencies, the noise can be further reduced by reading out the coil current directly.

7Noise through L:lx input-referred [V/sqrt(Hz)]

1e-07

1e-08

1e-09

1e-10

1e-11
10

100

OP UNoise(op1)

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Frequency [Hz]OP INoise+(op2)

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100000Sum Noise

Figure 9: Noise of the coil driver circuit (see text).

In this situation, the noise added by the coil driver will be suppressed by the open-loop
gain. However, the read-out amplifier will add extra noise of its own.
Figure 10 shows the circuit diagram of the readout amplifier (unchanged by thepresent author) and Figure 11 its transfer functions.
The two curves labeled ’a2’ and ’a3’ in Figure 12 show the additional noise generated by the readout amplifier, i.e. the noise generated by the components shown inFigure 10, again with and without the additional 50 Ω readout resistor. The noise√√at 1000 Hz is 1.85 nV/ Hz (without) and 0.92 nV/ Hz (with 50 Ω), respectively. Forcomparison, the curve labelled ’a1’ shows the total noise of the coil driver without theadditional 50 Ω readout resistor (same as in Figure 9).
The noise reduction achievable by using the readout amplifier as compared to measuring directly at the coil drivers input is not very big. If necessary it may be possible
to build a readout amplifier with lower noise by using an audio transformer. However,this will only be worthwhile when the coil driver noise is a significant contribution tothe overall interferometer noise.

8Figure 10: Readout amplifier.

100AbsPhase [Degree]

101

00.1
0.11101001000
Frequency [Hz]10000100000

1e+06

U(no4) [V/V] Abs

U(no3) [V/V] Abs

Figure 11: Transfer functions of the readout amplifier (DC and AC outputs, with additional
50 Ω readout resistor).

9

Noise at node no4 input-referred [V/sqrt(Hz)]

1e-07

1e-08

1e-09

1e-10
10

Sum Noise a1

1001000
Frequency [Hz]Sum Noise a2

10000100000

Sum Noise a3

Figure 12: Noise generated by the readout amplifier (’a1’ and ’a2’ with and without theadditional 50 Ω readout resistor, respectively) compared to noise of the coil driver (’a0’).

107Output impedance

In order to avoid damping of the pendulum, the output impedance of the coil drivershould be high (ideally, a current source has infinite output impedance). Figure 13
shows the output impedance of the new driver circuit.

1e+06
0Abs

10000
-451000

Phase [Degree]

100000100

1010100

1000
Frequency [Hz]10000-90100000

Zin [Ohm] Phase

Zin [Ohm] Abs

Figure 13: Output impedance of the coil driver circuit (see text).

For the damping of the pendulum the real part of the impedance is important. Itis shown in Figure 14. At 1 kHz, its value is about 300 kΩ.

111e+09
1e+08
1e+07
1e+06

Re100000
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1000
100
10
1101001000
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Frequency [Hz]1000001e+06

1/I(lx) [V/A] ReFigure 14: Real part of the output impedance of the coil driver circuit (see text).

12