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Traffic Detector Handbook:Third Edition—Volume II

APPENDIX H. DIGITAL PERIODSHIFT ELECTRONICS UNIT ANALYSIS

ABSTRACT

Appendix H describes the derivation of the digital period-shift electronics unit sensitivity, which is shown to be proportional to the threshold count N_pt divided by the total number of counts N_pc in the frequency counter. The response time is proportional to the threshold count, divided by the product of the sensitivity and the frequency of the crystal clock.

ANALYSIS

The oscillator in a digital period-shift electronics unit operates at a frequency f_D, which is determined by the loop, lead-in cable, and the electronics unit tuning network. The number m of oscillator cycles from the period scaler determines the length of the gating pulse applied to the AND gate. When the gating pulse is m times as long as the loop is occupied, more clock pulses are sent to the period counter, making the electronics unit more sensitive.

A simplified block diagram of a single channel, digital period-shift vehicle electronics unit is illustrated in Figure H-1. The change in inductance at the electronics unit terminals caused by a vehicle produces a change in the oscillator frequency. The sine wave oscillator frequency is converted by a period scaler into a square wave. The square wave is input to an AND gate, which compares the signal level (i.e., high or low) to that of the crystal clock frequency pulse.

Figure H-1. Digital period-shift electronics unit block diagram.

If both the square wave and the crystal clock pulse are high, a count is sent to the period counter. The count is equal to the number of clock pulses that occur in a period.

At the end of the period, the count is sent to the first comparator. The comparator subtracts the reference period count stored in memory, which represents the count when no vehicle is present, from the current period count. The difference enters the second comparator. If the second comparator finds that the difference is in excess of the threshold sensitivity, then a vehicle is presumed present and a call is output.

The period T_DC of the electronics unit oscillator is

(H-1)

The length of the gating pulse is

(H-2)

The number N_pc of clock pulses counted by the period counter is

(H-3)

where T_C is the period of the crystal clock equal to the inverse of the clock frequency.

The number of clock pulses stored in the reference memory when no vehicle is present is

(H-4)

The number of clock pulses counted when a vehicle is present is

(H-5)

Since the loop inductance decreases when a vehicle is sensed, the electronics unit oscillator frequency f_D increases and the oscillator period T_D decreases. Then

(H-6)

The output of the first comparator is

(H-7)

Since

(H-8)

the output of the first comparator can be written as

(H-9)

When the output count ΔN_pc of the first comparator equals the threshold count N_pt in the second comparator, a vehicle call results.

Then,

(H-10)

Thus,

(H-11)

For a high quality factor tuned circuit, the normalized period shift is approximated by

(H-12)

Solving for sensitivity, we get

(H-13)

(H-14)

Since

(H-15)

and

(H-16)

(H-17)

when

(H-18)

(H-19)

Letting

(H-20)

the sensitivity becomes

(H-21)

since

(H-22)

from Equation H-3,

(H-23)

The response time of the digital period-shift electronics unit is primarily due to the time required to fill the period counter with clock pulses. Thus,

(H-24)

Rewriting equation H-23 to solve for N_pc, we get

(H-25)

Upon substituting this result into equation H-24, the response time becomes

(H-26)

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