Figure out, you conceive a powerful digital sensor and you want to use it with the LEGO RCX. You must transform the digital information to an analog signal. Generally this is done through a special IC. While such a solution is the easiest for engineers, amateurs may have difficulties in finding the optimal chip, or may be limited in budget. We already presented a crude 8-bit converter based on a simple resistor-net.

Here now two other types of converters.

The LEGO-Mindstorms project in an educational context rapidly shows its power around heuristic thinking. In team-discussions about solving a problem, several approaches appear in concurrence. The team must proceed to an evaluation, which solution is the best. In the case of deciding if the team should prefer a D/A-integrated circuit to another solution, different arguments must be weighted such as efficiency, speed, costs, simplicity, space needed on the PC-board, choice of micro-controller (if ever), number of micro-controller I/O's available, and so on. For example, sometimes you need only a rather slow conversion, but you want to spare some room on the board and you want to work with one of the cheapest PICs. In this case you'll use the following device.

1. Pulsing D/A converter (Integrator)

A PIC (16F84) is driven at 4 MHz. One I/O-pin is configured to be an output. The idea is to generate a pulse at a given duty x%. This signifies that the pin is set to 1 (=5V) during x% of the period and to 0 (=0V) during (100-x)% of the period. The PIC-pin is buffered through an operation amplifier which changes the impedance. Then the signal is led to an RC-cascade. The couple R1-C1 integrates the signal. This means that the capacitor C1 is charged during x% of the time then discharged during (100-x)% of the time.

Suppose the capacitor's voltage is zero initially. As the charge rate depends on the charge time, the initial voltage and the time constant T=RC, every cycle the capacitor is not completely discharged. To be precise only (100-x)% of the charge is lost.

Example: x=50%, the voltage after one cycle is either 1.25 or 3.25 V depending on the capacitor's initial state. This is half of the charge. (The timerate in the picture does not correspond to R₁C₁!! It is only an illustration of what is going on)

The R2-C2 / R3-C3 cascade filters the signal.

If we choose y as a value of the interval 0 .. 255 with x = y / 256,  we'll divide one cycle into 256 segments. Thus we may transform any byte-number to a proportional voltage.

At 4MHz, the internal PIC program counter is incremented at 1 MHz. Deviding into 256 segments gives a frequency of 3.9kHz. As you can see in the following pictures, the voltage is stabilized around the duty-percentage after about 6ms. By choosing other values of R1, R2, R3, C1, C2 or C3, it is possible to have a quicker respons. You'll have to make a compromise between speed and signal-stability. 

Note that the charging of a capacitor obeys to the formula:

The discharging has the formula:

Constantly driven, the capacitor is charged to 98% resp. discharged to 2%  after 4t.

Note that you should test the RC-cascade with an oscilloscope or an electronic simulator on your PC.

Conclusion:

We get a direct proportional relationship between duty-percentage and the output voltage.

Here a (not too elegant) PIC test-program for a 50% duty pulse.

     LIST  P=16F84
;
PORTA    EQU    5
PORTB    EQU    6
TRISA    EQU    85H
TRISB    EQU    86H
STATUS   EQU    3
INTCON   EQU    0BH
OPTREG   EQU    81H
TMR0     EQU    1

CY       EQU    0
RP0      EQU    5
TOIF     EQU    2
TOIE	 EQU	5
GIE	 EQU	7

#DEFINE  BANK0  BCF  STATUS,RP0   ;SELECT BANK 0
#DEFINE  BANK1  BSF  STATUS,RP0   ;SELECT BANK 1

;********************************************************

	 ORG 	0
	 GOTO 	START

	 ORG 	4
	 COMF 	PORTB,F	    ;INVERT PORTB
	 BCF	INTCON,TOIF ;CLEAR INTERRUPT FLAG
         RETFIE

LOOP	 GOTO 	LOOP        ;DO NOTHING FOREVER
	 

START	 BANK1
	 CLRF   TRISA^80H   ;PORTA ALL OUTPUTS
	 CLRF	TRISB^80H   ;PORTB ALL OUTPUTS	
	 MOVLW  B'00000001' ;TIMER0 PRESCALE 1:2
	 MOVWF  OPTREG^80H
	 BANK0

	 CLRF 	PORTA
	 CLRF 	PORTB
	 BSF	INTCON,TOIE ;ALLOW TIMER INTERRUPT
	 BSF	INTCON,GIE  ;ALLOW ALL INTERRUPTS
	 CLRF	TMR0
	 BCF    INTCON,TOIF ;CLEAR INTERRUPT FLAG 
	 GOTO   LOOP 

         END

2. Resistor-net

Trying to understand this astute resistor-net designed to transform a digital port-value to an analog signal is a very interesting didactical exercise. The trick is to combine resistors of only two different values R and 2R in such a way that the net finally gives the exact voltage-output which is proportional to the PIC output-value. The respons of this converter is very quick compared to the former example, but instead you need more than one PIC output-pin, according to the desired accuracy.

For better understanding here a three-bit example: 

HINT: analyse the pictures in the order:

port_value=0, port_value=4, port_value=2, port_value=1

As you can see, the sub-systems of the nets are always parallel or serial resistors of values:

2R = R + R  or  R = 2R*2R/(2R+2R) or more complex combinations.

Main Page