9. Notes on Feedback Control Loops with the DigiLock 110
Page 41
Status: 5.12.17
9 Notes on Feedback Control Loops with the DigiLock 110
The DigiLock 110 is a universal module to realize different locking scenarios. It provides two PID controllers,
means for frequency modulation techniques as well as tools for analyzing the lock. This section is
indented as a starting point for more detailed information on the integration of control loops and their
optimization. For application examples see section 10. Before discussing the adjustment of the controller
parameters (section 9.3) it is helpful to consider a few signal path issues (section 9.1). Frequency modula-
tion is necessary to generate an error signal for top of fringe locking. It also offers advantages in terms of
insensitivity with respect to amplitude modulation and frequency noise and can provide a larger capture
range (section 9.2). The AutoLock mode of the DigiLock 110 relies on a consistent choice of polarity and
slope, the determination of which is discussed in section 9.4. Details of the relocking and signal analysis
features can be found in section 9.4 and 9.5, respectively.
9.1 Signal to Noise and Bandwidth Considerations
To take full advantage of the possible bandwidth of the control loop, care should be taken to implement
a true 50 Ohms wave guide and to avoid extra cable length in the signal path. The fast inputs and out-
puts of the DigiLock 110 are 50 Ohms in the standard setting upon delivery. If necessary, they can be
changed to high impedance by appropriate settings of internal jumpers (for details please see section
11.2). Bandwidths and sampling rates of the inputs and outputs are listed in Table 8.
Due to the limited gain-bandwidth product in analog amplification, a higher gain generally reduces
the bandwidth
3
. In the DigiLock 110 the digital signal paths do not show this effect, but instead every pro-
cessing step inherently contributes a fixed delay. The integration of extra filters, e.g. low-pass filters to
“clean-up” the error signal, usually has a negative influence by introducing extra phase lag and should
hence be avoided. Improvements based on filters usually rely on a detailed analysis of the frequency
response of the control loop and have to be designed carefully. For most cases it is recommended to
bypass the digital input filters in the System (see section 8.2.4).
To optimize the signal to noise ratio of the input, subtract the dc offset from the input signal by setting
the input offset in the System (see Figure 19) to the mean value as read from the oscilloscope display or
the negative if inversion is activated in the System. The gain can now be increased to take advantage of
the full +/-2 V range of the analog-to-digital converter.
9.2 Frequency Modulation Techniques
Frequency modulation techniques are applied to obtain an error signal with a steep slope at the lock
point. The typical spectroscopy signal in transmission or absorption consists of a resonance line, e.g. a
Lorenzian or Gaussian or multiple thereof (see application examples in section 10). To lock to the maxi-
mum of the resonance a dispersive signal is needed, which is generated by frequency modulation and
subsequent demodulation. There are two regimes depending on the choice of the modulation fre-
quency with respect to the characteristic line width Dn of the resonance:
A modulation frequency ν
mod
smaller than ∆ν leads to the derivative of the resonance signal as
obtained from the Lock-In module (cp. section 10.2.2)
4
.
A modulation frequency much larger than ∆ν (cp. Pound-Drever-Hall, section 10.3) will lead to an
error signal – and hence capture range – that extends from one sideband to the other [ν
0
- ν
mod
, ν
0
+
ν
mod
]. The latter situation is preferable and used in situations where the resonance is well isolated, e.g. on
a Fabry-Perot cavity where no neighboring resonances spoil the signal. In this case a higher modulation
frequency also provides a higher bandwidth error signal after mixing with the local oscillator (LO).
The phase of the local oscillator must be adjusted to obtain a large error signal with steep slopes at
the resonance of the spectral signal. The sign of the error signal can be inverted by changing the phase
3. Note, that the analog preamplifiers in the DigiLock 110 have a fixed bandwidth independent of the selected gain.
NOTE ! Due to the specific design the input analog gain does not contribute an additional band-
width reduction.
4. Some details on the generation of the error signal by frequency modulation can be found in the SYS DC 110 manual in the
corresponding chapters of LIR 110 and PDD 110, respectively.
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