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Publication Number: FHWA-HRT-06-139
Date: October 2006

Traffic Detector Handbook:Third Edition—Volume II

APPENDIX F. DIGITAL FREQUENCY-SHIFT ELECTRONICS UNIT ANALYSIS

ABSTRACT

Using a frequency counter, the frequency-shift electronics unit uses the change in inductance caused by a vehicle passing over a loop to measure the altered electronics unit oscillator frequency.

Appendix F describes the operation of the digital frequency-shift electronics unit, which measures the difference in oscillator frequency fD that occurs with and without a vehicle present. A frequency counter computes the frequency difference by determining a count difference that is proportional to the frequency difference. The frequency-shift electronics unit sensitivity is shown to be proportional to the threshold count Nft divided by the total number of counts Nfc in the frequency counter.

ANALYSIS

A simplified block diagram of a single-channel, digital frequency-shift electronics unit is illustrated in Figure F-1. The change in inductance at the electronics unit terminals causes a change in the oscillator frequency. The frequency is multiplied by the frequency multiplier. The resultant frequency is transformed into a frequency count by the frequency counter.

Figure F-1 shows that in a frequency shift electronics unit, the change in inductance at the detector terminals causes a change in the detector oscillator frequency. The frequency is multiplied by the frequency multiplier. The result is then counted by the frequency counter. The frequency counter was initialized to zero at the end of the previous frame count. This reset is done by a one-shot device. The device is activated by a divider of the clock frequency. This activates at the end of the frame time. The first one shot device causes a transfer of the frequency count while the second one-shot device causes the reset of the frequency counter. At the end of the frame time, the count of the frequency is sent to the comparator. The comparator subtracts the frequency reference memory with no vehicle present from the frequency count. The difference is then sent to the second comparator. This is a comparison of the current sensor frequency state to the frequency state with no vehicle present. If the second comparator finds that the frequency difference is in excess of the threshold sensitivity then a vehicle is presumed present and a call is output.

Figure F-1. Digital frequency-shift electronics unit block diagram.

The frequency counter is first initialized to zero. Frequency count data are then collected for a preset time frame. The first one-shot module then causes the frequency count to be transferred to the frequency counter and first comparator at the end of the time frame. The second one-shot module resets the frequency counter to zero so that it can collect data for the next time frame. The cycle then repeats.

The first comparator subtracts the reference frequency count stored in memory, which corresponds to the count when no vehicle is present, from the frequency count just transferred, which may or may not correspond to the presence of a vehicle. The count difference is next sent to the second Output Call comparator. If the second comparator finds that the count difference is greater than the threshold sensitivity count, then a vehicle is presumed present and a call is output.

The reference frequency count in memory updates at a specified time interval whenever no change has occurred in the call status over that interval.

The number of oscillator cycles counted by the frequency counter is

Equation F-1. Capital N subscript lowercase f lowercase c is equal to the product of lowercase m multiplied by lowercase f subscript Capital D multiplied by capital T subscript lowercase f lowercase t which in turn is equal to the quotient of the product of lowercase m multiplied by lowercase f subscript capital D, divided by lowercase f subscript lowercase n lowercase c. (F-1)
where
Tft= frame time of the frequency counter in s
m= frequency multiplier
fD= frequency of electronics unit oscillator in Hz
fnc= crystal clock frequency in Hz.

The frame time is assumed to be constant at each sensitivity setting. The response time of the digital frequency-shift electronics unit is equal to the frame time Tft, which in turn is equal to the inverse of the divided crystal clock frequency.

For example, with a frame time of one second, the number of counts Nfc made by the frequency counter is the electronics unit oscillator frequency multiplied by m.

Since the frequency of the electronics unit oscillator changes when a vehicle is present, the count given by the frequency counter will also change. Thus, the presence of a vehicle is ascertained by noting when the change in the output of the frequency counter is above some threshold.

The reference count is measured with no vehicle present and is equal to

Equation F-2. Capital N subscript lowercase f lowercase c superscript lowercase n lowercase v is equal to the quotient of the product of lowercase m multiplied by lowercase f subscript Capital D superscript lowercase n lowercase v, divided by lowercase f subscript lowercase n lowercase c. (F-2)

With a vehicle present, the count becomes

Equation F-3. Capital N subscript lowercase f lowercase c superscript lowercase v is equal to the quotient of the product of lowercase m multiplied by lowercase f subscript Capital D superscript lowercase v, divided by lowercase f subscript lowercase n lowercase c. (F-3)

The electronics unit computes the difference in count ΔNfc with and without a vehicle present at the output of the first comparator as

Equation F-4. Delta Capital N subscript lowercase f lowercase c is equal to the difference between Capital N subscript lowercase f lowercase c superscript lowercase v minus Capital N subscript lowercase f lowercase c superscript lowercase n lowercase v. (F-4)

Substituting Equations F-2 and F-3 into the above equation yields

Equation F-5. Delta Capital N subscript lowercase f lowercase c is equal to the difference between the quotient of the product of lowercase m multiplied by lowercase f subscript Capital D superscript lowercase v, divided by lowercase f subscript lowercase n lowercase c, minus the quotient of the product of lowercase m multiplied by lowercase f subscript Capital D superscript lowercase n lowercase v, divided by lowercase f subscript lowercase n lowercase c. (F-5)

Factoring out m and fnc yields

Equation F-6. Delta Capital N subscript lowercase f lowercase c is equal to the product of the quotient of lowercase m divided by lowercase f subscript lowercase n lowercase c, multiplied by the difference between lowercase f subscript capital D superscript lowercase v minus lowercase f subscript capital D superscript lowercase n lowercase v. (F-6)

Denoting (fDv - fDmv) by ΔfD, we get

Equation F-7. Delta Capital N subscript lowercase f lowercase c is equal to the quotient of the product of lowercase m multiplied by delta lowercase f subscript capital D, divided by lowercase f subscript lowercase n lowercase c. (F-7)

as the difference in count that occurs when a vehicle is present and not present.

A vehicle call is output when the difference count ΔNfc equals the threshold count Nft.

Accordingly when a call is made, one can write

Equation F-8. Delta Capital N subscript lowercase f lowercase c is equal to Capital N subscript lowercase f lowercase t. (F-8)

or

Equation F-9. Capital N subscript lowercase f lowercase t is equal to the quotient of the product of lowercase m multiplied by delta lowercase f subscript capital D, divided by lowercase f subscript lowercase n lowercase c. (F-9)

From Equation 2-51 in Chapter 2, the sensitivity of the digital frequency shift electronics unit is given by

Equation F-10.Capital S subscript Capital D superscript lowercase f is equal to the product of negative 2 multiplied by the quotient of delta lowercase f subscript capital D, divided by lowercase subscript capital D. (F-10)

Upon substituting ΔfD from Equation F-9 into Equation F-10, we obtain

Equation F-11. Capital S subscript Capital D superscript lowercase f is equal to the following quotient. The numerator is equal to the product of negative 2 multiplied by Capital N subscript lowercase f lowercase t multiplied by lowercase f subscript lowercase n lowercase c. The denominator is equal to the product of lowercase m multiplied by lowercase f subscript capital D. (F-11)

Since

Equation F-12. Lowercase f subscript capital D is equal to the quotient of one divided by the product of 2 multiplied by pi multiplied by the square root of the product of Capital L subscript Capital D multiplied by Capital C subscript Capital D. (F-12)

the sensitivity becomes

Equation F-13. Capital S subscript Capital D superscript lowercase f is equal to the following quotient. The numerator is the product of negative 4 multiplied by pi multiplied by Capital N subscript lowercase f lowercase t multiplied by lowercase f subscript lowercase n lowercase c multiplied by the square root of the product of Capital L subscript Capital D multiplied by Capital C subscript Capital D. The denominator is equal to lowercase m. (F-13)

Thus, the sensitivity of the digital frequency-shift electronics unit is directly proportional to the threshold frequency count Nft, the crystal clock frequency fnc, and the square root of the product of the total inductance LD across the electronics unit terminals and total capacitance CD across the electronics unit terminals (CD includes internal tuning capacitance). Sensitivity is inversely proportional to the oscillator multiplier factor m.

An equivalent electrical circuit showing the inductive and capacitive elements that contribute to LD and CD is shown in Figure F-2.

Figure F-2 shows that the lead-in cable inductance plus the loop inductance is equivalent to the inductance in a tank circuit which is coupled with a detector capacitance which in turn feeds the active device circuit. This yields the output frequency of the oscillator. The resonant frequency for this tank circuit is described in equation F-12.

Figure F-2. Loop-inductive and capacitive elements at electronics unit terminals.

If we define

Equation F-14. Capital K subscript lowercase f is equal to the following quotient. The numerator is equal to the product of negative 4 multiplied by pi multiplied by Capital N subscript lowercase f lowercase t multiplied by lowercase f subscript lowercase n lowercase c. The denominator is equal to lowercase m. (F-14)

then

Equation F-15 NEW VERSION. Capital S subscript Capital D superscript lowercase f is equal to the product of Capital K subscript lowercase f multiplied by the square root of the product of Capital L subscript Capital D multiplied by Capital C subscript Capital D. (F-15)

Another form for the sensitivity equation is obtained by substituting

Equation F-16 NEW VERSION. Capital N subscript lowercase f lowercase c is equal to the quotient of the product of lowercase m multiplied by lowercase f subscript Capital D, divided by lowercase f subscript lowercase n lowercase c. (F-16)

from Equations F-2 or F-3 into Equation F-11 as

Equation F-16 NEW VERSION. Capital N subscript lowercase f lowercase c is equal to the quotient of the product of lowercase m multiplied by lowercase f subscript Capital D, divided by lowercase f subscript lowercase n lowercase c.

or

Equation F-17.Capital S subscript Capital D superscript lowercase f is equal to the quotient of the product of negative 2 multiplied by Capital N subscript lowercase f lowercase t, divided by Capital N subscript lowercase f lowercase c. (F-17)

Thus, the frequency shift electronics unit sensitivity is proportional to the frequency threshold count Nft divided by the total number of counts Nfc in the frequency counter.

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