Galil DMC-3425 user manual Dac, Digital Filter

DAC

The DAC or D-to-A converter converts a 16-bit number to an analog voltage. The input range of the numbers is 65536 and the output voltage range is +/-10V or 20V. Therefore, the effective gain of the DAC is

K= 20/65536 = 0.0003 [V/count]

Digital Filter

The digital filter has three elements in series: PID, low-pass and a notch filter. The transfer functions of the filter elements are:

PID	D(z) =	K(Z − A)	+	CZ
		Z		Z − 1

Low-pass	L(z) =		1 − B
		Z − B
			(Z − z)(Z −		)
Notch	N(z) =			z
			(Z − p)(Z −			)
				p

The filter parameters, K, A, C and B are selected by the instructions KP, KD, KI and PL, respectively. The relationship between the filter coefficients and the instructions are:

K = (KP + KD) ⋅ 4

A = KD/(KP + KD)

C = KI/2

B = PL

The PID and low-pass elements are equivalent to the continuous transfer function G(s). G(s) = (P + sD + I/s) ∗ a/(S+a)

P = 4KP

D = 4T ⋅ KD I = KI/2T

a = 1/T ln = (1/B) where T is the sampling period.

For example, if the filter parameters of the DMC-2x00 are KP = 4

KD = 36

KI = 2 PL = 0.75 T = 0.001 s

the digital filter coefficients are

164 • Chapter 10 Theory of Operation DMC-3425