Instrumentation & Measurement Magazine 23-2 - 99

Sidebar: A Simple Analysis of the
Summing Circuit
The simplest way to analyze the summing circuit (Fig.
3) is to make use of superposition. Note that V1 and V2
are connected to the circuit in the same way, so that once
one's influence has been analyzed, so has the other's.
Let's ground V1 and see how V2 influences the output. As (essentially) no current flows into an op-amp,
the voltage at the non-inverting input of the op-amp
will be V2/2. Assuming the op-amp circuit was properly designed, this will also be the value at the inverting
input. This will cause a current of V2/(2 Ra) to flow in
the upper branch of the circuit, and it is easy to see that
causes the output voltage to be V2. As V1 and V2 affect
the output in the identical fashion, the output of this circuit will be V1 + V2.

The stored values are sampled by the ADuC841 microcontroller. The microcontroller samples one output of the "hold
circuit" of Fig. 1 every 1/1600 s, and this is the point at which subNyquist sampling occurs. The 975 Hz signal is located above 800
Hz-above the Nyquist frequency associated with the microcontroller's sampling rate. The microcontroller's A/D converts
one analog value to a digital value every 1/1600 s, and then the
microcontroller transmits the data to a PC using the microcontroller's UART. A UART to USB adapter is used to convert the
microcontroller's output into a signal that uses a protocol our
PC understands and to allow the PC to communicate with the
microcontroller.
The full schematic of the system (other than the PC) is given
in Fig. 4.
On the PC side there is a MATLAB program that knows how
to "talk" to the microcontroller (using the suite of serial-port
related commands supported by MATLAB). We have written
MATLAB code that identifies the frequency of the signal being
measured and reconstructs the un-compressed sample values.

Fig. 3. A simple summing circuit.

In Fig. 5, one sees a signal as measured by one stage of the
analog shift register, in Fig. 6, one sees the five samples of the
same signal as reconstructed by MATLAB, and in Fig. 7 ones
sees the whole system. The "input" to the MATLAB code (input gotten from the UART) was the four compressed samples.

The Devil is in the Details
There is practically no system so simple that there are no surprises when one implements the system. In this section, we
present one interesting problem we faced and describe a solution to the problem.
Because the ADuC841's A/D requires that its input be
positive, we had to add an offset to our sinusoids. Because the
phase of the sinusoid relative to the system was unknown, we
had to assume that any sinusoid would be a linear combination of a sine and a cosine. This meant that when inputting a
sinewave, we could not input anything else-we could not
input a sinewave and a constant because this would require

our x to have three non-zero components-one more than
we could handle. We had to "get rid of" the influence of the
offset.
In order to do this, we added a calibration phase in which
the user entered the fixed offset with no accompanying

Fig. 2. Two stages of a master-slave analog "shift register." This circuit uses op-amps as buffers and stores voltages on capacitors that are charged through
analog switches that are opened and closed by a clock. The master and slave use complementary clocks.
April 2020	

IEEE Instrumentation & Measurement Magazine	99



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