SECTION 13. CR10 MEASUREMENTS

discussed for minimizing input settling error

when long leads are mandatory.

FIGURE 13.3-1. Input Voltage Rise and Transient Decay
13.3.1 THE INPUT SETTLING TIME CONSTANT

The rate at which an input voltage rises to its full value or that a transient decays to the correct input level are both determined by the input settling time constant. In both cases the waveform is an exponential. Figure 13.3-1 shows both a rising and decaying waveform settling to the signal level, Vso. The rising input voltage is described by Equation 13.3-1 and the decaying input voltage by Equation 13.3-2.

V

s

= V

so

(1-e-t/RoCT), rise

[13.3-1]

 

 

 

 

 

 

V

s

= V

so

+ (V

eo

-V ) e-t/RoCT, decay

[13.3-2]

 

 

 

so

 

where Vs is the input voltage, Vso the true signal voltage, Veo the peak transient voltage, t is time in seconds, Ro the source resistance in ohms, and CT is the total capacitance between the signal lead and ground (or some other fixed reference value) in farads.

The settling time constant, τ in seconds, and the capacitance relationships are given in Equations 13.3-3 through 13.3-5,

τ = RoCT

[13.3-3]

CT = Cf + CwL

[13.3-4]

Cf = 3.3 nfd

[13.3-5]

where Cf is the fixed CR10 input capacitance in farads, Cw is the wire capacitance in farads/foot, and L is the wire length in feet.

Equations 13.3-1 and 13.3-2 can be used to estimate the input settling error, Ve, directly. For the rising case, Vs = Vso-Ve, whereas for

13-4

the decaying transient, Vs = Vso+Ve. Substituting these relationships for Vs in Equations 13.3-1 and 13.3-2, respectively, yields expressions in Ve, the input settling error:

V

e

= V

so

e-t/RoCT, rise

[13.3-6]

 

 

 

 

V

e

= V

e'o

e-t/RoCT, decay

[13.3-7]

 

 

 

 

Where Ve'o = Veo-Vso, the difference between the peak transient voltage and the true signal voltage.

NOTE: Since the peak transient, Veo, causes significant error only if it is several times larger than the signal, Vso, error calculations made in this section

approximate Ve'o by Veo; i.e., Veo = Veo- Vso.

If the input settling time constant, τ , is known, a quick estimation of the settling error as a percentage of the maximum error (Vso for rising, Ve'o for decaying) is obtained by knowing how many time constants (t/τ) are contained in the 450 µs CR10 input settling interval (t). The familiar exponential decay relationship is given in Table 13.3-1 for reference.

TABLE 13.3-1. Exponential Decay, Percent of Maximum Error vs. Time in Units of τ
Time

%

Time

%

 

ConstantsMax. Error

Constants

Max. Error

0

100.0

5

0.7

 

1

36.8

7

0.1

 

3

5.0

10

0.004