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Half-flying Capacitor Analog Multiplexer
A method of multiplexing analog signals using a microcontroller's I/O pins.
Originally appeared in EDN/Reed Business Information January 22, 2004

Fig. 1 This is the test circuit (schematic below), in which LEDs
light when the voltage on corresponding input pots
exceed the voltage on a reference pot demonstrated
that the multiplexed inputs are independent. The board above
 includes a 6 pin programming header, a 2 pin ground test
point,  and a 5 volt regulator.

This technique uses digital  I/O pins to multiplex analog voltages into an analog input on the microcontroller. The method is most suitable for signals that do not need to be sampled frequently and it may be extended to accommodate a large number of inputs, though for a large number of inputs, the use of a separate analog multiplexer or a mincrocontroller with an integrated multiplexer would often be a better choice.

The test circuit (schematic below, photograph above), when running the associated firmware (click here to see the assembler code (file name "hfcm030602.asm"), compares two test voltages, appearing on the wires of the 10k pots, with a reference voltage, which appears on the wiper of the 50k pot. When a test voltage exceeds the reference voltage, the LED corresponding to that particular test voltage lights, demonstrating that the two sampled channels are independent.

Fig. 2 Pins 12 and 13 are inputs to the comparitor.

The AT90S1200A used for the test has a single comparitor, but an analog multiplexer was formed using two of its digital bidirectional I/O ports. Notice that for each analog input, there is a 100k resistor, a .01 uf capacitor, and a diode. The resistor-capacitor combination form a low pass filter and switching of the charged capacitor is the means by which multiplexing is effected.

Here is how it works

Fig. 3 Bidirectional I/O pin used to ground comparitor input

The technique takes advantage of bidirectional I/O ports to switch from outputs to inputs. In the case of many AVR controllers, the input of the comparitor shares a pin with a bidirectional I/O bit. This allows the pin to be held at ground and then ungrounded when using it as an input for the comparitor.

Fig.4 Various states of one channel.

Most of the time, the circuit is in the "filtering" sate (see the illustrations above). The inputs are sampled periodically at a low duty cycle as the sampling duty cycle affects cross talk among the inputs. This is discussed in more detail below. During filtering time, pin 12, which is the input to the comparitor is held at ground and pin 12 (the I/O pin is an output,  written with a logic low), Pin 14, which is the multiplexing pin, is open. Under these conditions, the filter capacitor is kept charged to the input voltage (V1).

When it is time for the input voltage to be connected to the comparitor input, pin 12 is opened (the I/O pin is made into an input) and the multiplexing pin, pin 14, is connected to + 5V (made into an output pin and written with a logic high). This causes the positively charged plate of the capacitor to be connected to +5V through the diode. This results in a a Vdd minus one diode drop, minus the voltage on the capacitor being applied to pin 12.

Vpin12 = Vdd - Vdiode - Vin
Vpin12 = the voltage applied to the analog input of the comparitor, pin 12,
Vdd = the power supply voltage, 5 volts in this example,
Vdiode = the voltage drop across the diode, which is somewhat dependent on the current through the input resistor, and
Vin = the input voltage applied to the input of the RC filter.

One thing that should be apparent from looking at the expression above, is that input voltages are restricted to the range of 0 volts to Vdd-Vdiode, or 0 to about 4.4 volts. As voltages approach 4.4 volts, the current through the diode will become very low, and a noticeable linearity may develop.

To make a multiplexer, simply combine two or more of these switched capacitor stages along with their control I/O pins, as shown in the illustration below.

Fig. 5. Two channel analog mux.

The diodes are necessary to provide isolation while the other channels are selected. In the third state illustrated below, the voltage V2 across a second channel is being sampled. If the V2 = 0 volts, and if V1 = 5V (so that the voltage across C1 = 5 volts), then when V2 is sampled, the cathode of the connected to pin 15 is one diode drop below the +5V supply, and that would put the positive plate of the C1 at about +9.4 volts. The diode in series with the multiplexing pins (14 and 15 in this example) is there to isolate the high positive voltages from the internal protection circuitry in the microcontroller.

As many channels as needed may be added by simply adding an additional resistor, capacitor, diode, and output pin for each channel.

Fig. 6. Four channel analog mux.

Other useful configurations include expanding the number of inputs. A 4:1 multiplexer is shown above. Multiple voltages within a single channel can be multiplexed without using more I/O pints, as in the example below, in which both inputs of the comparitor are multiplexed.

Firmware to switch and sample the comparitor's input
The routine below is called by a timer interrupt every 2048 clock cycles.

cbi DDRB,0 ;+ Input to comparitor high Z.

sbi PORTB,2 ; Input 1 pin logic high.
nop ; Wait 1 microsecond for comparitor to settle.
in LED1,ACSR ; Copy comparitor state to memory.
cbi PORTB,2 ; Input 1 pin logic low.

sbi PORTB,3 ; Input 2 pin logic high.
nop ; Wait 1 micrsecond for comparitor to settle.
in LED2,ACSR ; Copy comparitor state to memory.
cbi PORTB,3 ; Inputnel 2 to logic low

sbi DDRB,0 ; + Input of comparitor to ground.

In the above code fragment, LED1 and LED2 refer to internal RAM registers associated with inputs 1 and 2 respectively. Care must be taken to make the I/O port bit associated with the comparitor input into an input before switching the signals to the diodes, else the voltage across the capacitors be disturbed. Then entire source code for the AT90S1200A is included in the file hfcm030602.asm.

Mischarge if filter capacitor and resulting error

It is important to keep the time in the "sampling" and "other channel being sampled" states to a minimum percentage of the total period of the measurement, and also to keep these times short compared to the time constant of the RC filter, because the charge on the capacitor associated with each channel is affected during the measurement of other inputs, which results in cross talk.

Fig. 7.  The illustration above is useful in establishing terminology used in the discussion below.

To explain this, I am going to refer to input 1. If all the times and component values for input 2 are the same, then the discussion applies equally to input 2. This discussion also applies to multiple channels, though the details would need to be modified to accommodate the specific implementation. Calculations represent very close engineering approximations.

During the filtering period (see figures 4 and 6) the input resistor and associated capacitor are connected as a low pass filter. During the time input 1 is being sampled, the voltage across C1 does not change. During the sampling of input 2, the voltage on C1 is disturbed by a "mischarge" through R1. The formulae to analyze this depend upon the type of input filter used. A fast filter, in which the RC time constant of the filters is small compared to the total measurement cycle time (Tcycle in Fig. 7) will allow more responsiveness in detecting voltage changes. Filters with long RC time constants compared to Tcycle can give better accuracy at the expense of responsiveness. The point at which one gives better accuracy than the other depends on the actual Tcycle, T1, and T2 times. Ways to analyze both are described.

If the time constant of R1C1 is large compared to the total measurement cycle time,  the amount of mischarge (cross talk) is proportional to the ratio of the input voltage times its duty cycle to the other channels voltages times their duty cycles. The maximum cross talk voltage,     Vmc1max =(Vdd - Vdiode) (T2/(Tcycle)

Vct = volts across C1 (output of multiplexer) resulting from mischarge during sampling of other channels,
Vdd = power supply voltage,
Vdiode = voltage drop across multiplexing isolation diode,
T2 = time in which input 2 is sampled, and
Tcycle = the period of one total measurement cycle.

This shows how measurement frequency can be traded against mischarge. Keep the measurement periods (T1, T2, etc.) as short as possible and keep the measurement cycle (Tcycle)  as long as necessary to maintain the required isolation between channels.

The mischarge error across C1 for a given case can be found by: Vmc1 =( (V2-Vdd-VC2) T2)/(Tcycle-(T1+T2))


Vmc1 = mischarge voltage error across C1,
V2 = voltage into input 2 of the multiplexer (V2 in figure 5),
Vdd = power supply voltage,
T2 = time in which input 2 is sampled,
Tcycle = the period of one total measurement cycle, and
T1 = time in which input 12 is sampled.

It is practical to use the expression for Vmc1max for design purposes and the expression Vmc1 for the purpose of analysis.

In the example code, interval between measurements are 2048 clock cycles, as set by the timer interrupts, and the time spent measuring each channel is 3 clock cycles. Accordingly, with Vdd = 5.0 volts, and assuming Vdiode = 0.5 volts, the maximum offset is  6.6 millivolt, or 0.15% of the 4.5 volt full span signal.

If the RC time constant of the input filter short compared to the total cycle time, then the mischarge error can be calculated using the exponential resistor-capacitor charging formula. In the case of a two input multiplexer, the worst case occurs on the second channel to be sampled, which in the case of this example is input 2. At the end of the charging period, C2 is charged to Vin2. During T1, the voltage across C2 changes as C1 is switched to Vdd.. The worst case is when Vin1 = 0 volts, so that there are 0 volts across C2, and the voltage on the negative end of C1 change by VDD-Vdiode. C1 And C2 are in series, so if their capacitances are equal, the effective capacitance = C2/2 and the voltage change across C2 is half the total voltage change across the series capacitance. The maximum error,

Verror = (Vdd-Vdiode) (1 - (exp ( -T1 / ( R2 ( C2 / 2) ) ) ) ) / 2

In the case of this example, where the input filters are made of 100k resistors and .01 uf capacitors, Vdd = 5.0 VDC, Vdiode = 0.5 volts, and T1 = 3 microseconds (1 MHz clock for the microcontroller), the maximum error is 13.5 millivolts, or 0.3% of the 4.5 volt full span signal.

One other effect to take note of, is that the switching signal will appear on the inputs of the multiplexer. This will range from zero to (Vdd-Vdiode) peak-to-peak through the input resistor. This may have an effect on the circuit being monitored.

The result of a test

The data below was measured on the test circuit:
1. Set Vin.
2. Adjust Vref just until the LED associated with Vi illuminated.
3. Record Vref voltage.


    Table 1. Test data.

The measured data are plotted in the graph below, along with the best fit for a linear transfer function. I suspect the small non linearity is the result of the diode drop varying with the input voltage.

Fig. 8. Plotting test data against best linear fit shows that the transfer function is inverted and  fairly linear.

One way to deal with the inversion and offset of the input voltage is to design the circuit so that the comparison value expects this. Another way to deal with this is to multiplex the other input on the comparitor. If you are multiplexing an A/D converter you'll have to compensate for the inversion and offset while handling the data.

Fig. 9. 2X2 Mux.

The configuration shown in figure 4 multiplexes both inputs of the comparitor. The result is that the polarity and offset drift resulting from the diode drop is largely compensated for. The implementation does not have to be restricted to two channels.

Fig. 10. Two channel A-to-D converter

The configuration shown in figure 5 shows how to make a multiple channel A-toD converter.  In this case, R1C1 and R2C2 form long time constant filters and R3C3 have a short time constant so as to make a fast negative going sawtooth with which to compare the input voltages with. See Atmel's' application note AVR-400 for the theory of operation of this kind of converter, or see this project on this web site for an example of this kind of converter with a negative-going sawtooth.

If an additional I/O port is available to reset the capacitor, one of the diodes can be eliminated.

Contents ©2003,2004 Richard Cappels All Rights Reserved. http://projects.cappels.org/
This web page frist posted in February, 2004.

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