The choice of a periodic bias results from the desire to avoid the contamination of the useful signal by low frequency noises of electrical origin, which is critical for instruments that cannot benefit from a high frequency optical modulation, such as the COBRAS/SAMBA project (Bersanelli et al. 1996). Unlike the systems proposed by Lange et al. (1996), which use a sine wave bias, the system presented here uses a square wave bias. This means that the electrical power dissipated in the bolometer is constant, and therefore the temperature of the bolometer does not oscillate. In consequence, there is no low frequency limit associated with the thermal time constant of the bolometer, and the well developed theory of DC biased bolometers can be directly used. A second original feature of this new system is that the bias is applied with opposite phases to the bolometer and to the load resistor. It is then possible to tune the amplitude of both bias voltages to obtain a signal near zero at the middle point and an optimal operating bias of the bolometer.
Figure 2: Electric modulation system for bolometers with a resistive
load (Diabolo, May 1994; left) and with a capacitance load (Diabolo,
March 1995; right)
In practice, two very stable square wave voltages of opposite sign (see
Fig. 2 (click here), left) are applied to both ends of the bolometer-load
resistor bridge,
and the middle point is connected to the pre-amplifier. The value of the load
resistor 
has to be very large in comparison with the bolometers resistance
(
), in order to determine a nearly constant electric current
(Mather 1982). It is possible to adjust the two bias
voltages 
and 
, in such a way that the bridge is
well-balanced and that the bolometer is optimally biased for the current
application. The voltage 
at point S is then equal to zero. When
the bridge is not well-balanced, due for example to a change in the
incoming radiation, the voltage at point S is given by:
It is then possible to measure the small changes of the voltage at point S due
to the small fluctuations of the bolometers resistor i.e., at first order:
Since and are square waves, is also a square
wave that can be amplified by a conventional pre-amplifier which includes
as a first stage a JFET at low temperature (
) used as a
follower. However, parasitic capacitances (C1, C2 and C3, due to
the resistors and the wires; see Fig. 2 (click here), left) introduce
transients (spikes) in at each step of the square wave, even when
the bridge is balanced. For a half-period of the bias, the shape of these
spikes is given by the following equation:
where 
is the output voltage at point S and, 
,
and 
are equal to:
, 
and 
.
The resulting spike is minimum when the following condition is fulfilled:
. This condition is generally not verified, but can be
approached by addition of a capacitance. In practice, it has been found simpler
to control the shape of the bias voltage in order to minimize the spikes and
the non linearities in the output signal (see the shape of the signal at point S
in Fig. 2 (click here)). If a residual transient still exists, it can be
discarded from the handled data by introducing a blank delay before integration
of the output signal at each half period in the lock-in amplifier.