Sigma-Delta Conversion Liquid Flow Switch Circuit
Xiang Zheng Tu
The present circuit comprises
all sigma-delta modulator necessary elements. Among them are an integrator, a
comparator, a 1-bit DAC, and a summing junction. The integrator function is acted
by a capacitor. The comparator plays as a 1-bite quantizer, which is built in a
microcontroller. The 1-bite DAC is a PWM outputted from the microcontroller,
which is resulted by filtering and emerging of the output of the comparator.
The summing junction combines the input signal and the PWM output, which is
carried out by a thermal flow sensor.
The thermal flow sensor is
micromachined to have a resistor heater and one or two thermopiles on a
suspended bridge created in a silicon substrate. The heater is located at the
central region of the bridge, where the temperature is raised above the
environment temperature by heating the heater. The hot and cold junctions of
the thermopile are located near the heater and the surrounding silicon frame,
respectively. The temperature difference between the central region and the
sounding frame is measured by the thermopile utilizing the Seebeck effect in which a thermal electromotive force is generated
in proportion to the temperature different.
It should be noted that the
thermal flow sensor is an inherent low pass filter. When the heater is heated by
a frequency change of the PWM output, the thermopile will take some time to
respond. A model of the response of the sensor can be based on a simple heat
transfer analysis. The rate at which the sensor exchanges heat with its
environment must equal the rate of change of the internal energy of the sensor.
Since in a fluid, the dominant mechanism of heat exchange is convection (neglecting
conduction and radiation), the energy balance is
hA(T∞ − T) = mc(dT/dt) , (1)
where h is the convection
coefficient, A is the surface area of the sensor, T is the temperature, m is
the bridge mass, and c is the bridge heat capacity.
Writing equation (1) in the form
τ (dT/dt) + T = T∞ , (2)
where the time constant is τ = mc/hA, which is the response of the
sensor reaching 63.2% of its final value. It has been obtained that the time
constant of the sensor is about 1ms or the cut-off frequency of the sensor is
about 1kHz.
In operation of
the present circuit, the capacitor integrates an input signal, so its output
passes a threshold voltage established with the comparator and the voltage
reference. The input signal is provided by the thermopile of the thermal flow
sensor with its heater by applying the PWM outputted from the microcontroller,
which is added a negative feedback signal from the output of the comparator.
The added signal is converted by the capacitor to a voltage that is presented
to one of the two inputs of a comparator. When the voltage passes the reference
voltage of the comparator the output of the comparator toggles between high and
low. The output is fed back to the input of the sensor via the PWM.
Additionally, the output of the comparator is fed forward to the digital filter
of the microcontroller. With time, the output of the digital filter provides a
bit stream result.
With the present circuit, the
thermal flow sensor can be operated in a constant temperature mode. The
reference voltage expresses the constant temperature that the heater is
expected to be heated. In order to do this, the PWM should be adjusted
carefully so that the thermopile produces the output exactly equal to the
reference voltage. Since the performance of the sensors may have
dispensability, zero offset is needed before fluid flow measurement. A bit
stream produced in the zero offset process represents no fluid flow. When a fluid
flow is conducted the temperature of the heater is reduced due to the fluid
flow cooling effect. The PWM needs to be adjusted again as to get the
temperature of the heater back to the original value.
The present circuit is an inexpensive and high resolution solution to the
thermal flow sensors for countless applications. In the circuit, the conversion
from analog to digital is performed with the internal-voltage reference,
comparator, and two counters in the microcontroller. These
internal-microcontroller analog peripherals, along with a thermal flow sensor,
are used to complete the implementation of a first-order modulator. This
modulator is then combined with an output-digital filter, which also is
implemented in the microcontroller unit, to complete the circuit. Consequently,
the only components external to the microcontroller are a thermal flow sensor, several
resistors, and a capacitor.