FM-CW Radar distance measuring apparatus

A FM-CW radar distance measuring apparatus, comprising a feedback loop having a high-frequency signal generator, a mixer device producing a beat signal between the transmitted wave and the received wave, a frequency discriminator, an integrator and a modulator which produces a sawtooth voltage for controlling the generator. The duration of the sawtooth is directly proportional to the distance to be measured. To improve the linearity of the signal to be transmitted a second (digital) feedback loop is provided, connected between the discriminator output and the modulator input and comprising the cascade arrangement of a threshold device, an adder, a store (and a digital-to-analog) converter. A distribution element connects the modulator to the store.

The invention relates to a FM-CW radar distance measuring apparatus, 
comprising a generator for a high-frequency signal whose frequency is 
linearly modulated by a modulator generating a sawtooth signal having a 
variable period T, which is in a linear relationship with the distance to 
be measured, means for transmitting a high-frequency signal to an object 
and means for receiving the high-frequency signal reflected from the 
object, a first feedback loop comprising a mixer stage to which the 
received signal and the transmitted signal are applied for generating a 
beat signal having a frequency f.sub.b, a frequency discriminator having a 
central frequency f.sub.o to which the beat signal is applied for 
generating an error signal which is applied to a first integrator circuit 
the output of which is coupled to an input of said modulator for adjusting 
the angle of inclination of the sawtooth signal to make the frequency 
f.sub.b substantially constant and equal to f.sub.o. 
As generally known, the accuracy of the distance measurement is influenced 
to a very high degree by the linearity of the sawtooth voltage generated 
by the modulator. For the above-described distance measuring apparatus 
this linearity is not only determined by the action of the modulator 
itself, but also by the shape of the object from which the transmitted 
high-frequency signal reflects. 
It is an object of the invention to reduce the influence of the shape of 
the object on the linearity of the sawtooth voltage, thus increasing the 
accuracy of the distance measurement. 
According to the invention this distance measuring apparatus therefore 
comprises: 
(1) a second feedback loop connected to the output of the frequency 
discriminator and comprising: 
- a level detector to which the output signal of the frequency 
discriminator is applied; 
- a second integrator circuit connected to the output of the level 
detector; 
(2) a combiner circuit included between the output of the first integrator 
circuit and the input of the modulator and arranged for combining the two 
signals produced by the two integrator circuits; 
(3) means for controlling the second integrator circuit and being 
controlled by the modulator output signal, these means generating within 
each period of the sawtooth voltage a same number of consecutively 
occurring control signals for generating a similar number of output 
signals of the second integration means.

The portion of FIG. 1 located to the right of the broken line A represents 
the prior art FM-CW distance meter. It comprises a high-frequency signal 
generator 1 having a control input which is connected to the output of a 
modulator 2. This generator 1 produces a high-frequency signal which is 
transmitted by means of an aerial 3. The reflected signal is received by 
an aerial 4 and is applied to a mixing stage 5, to which the transmitted 
signal is also applied thereby producing a difference signal. Via a 
low-pass filter 10 and an amplifier 7 this difference signal is applied to 
a frequency discriminator 6 which is tuned to a fixed frequency f.sub.o 
and produces an error signal whose magnitude is proportional to the 
deviation of the frequency of the difference signal relative to f.sub.o. 
This error signal is applied to an integrator 8 the output signal of which 
controls the slope of the sawtooth voltage generated by the modulator 2. 
If it is assumed that the amplitude of this sawtooth voltage is constant, 
then its period depends on its slope and, consequently, on the distance D 
to the object. For this distance D it now holds that: 
##EQU1## 
Herein .DELTA. F represents the constant frequency shift of the 
high-frequency signal; 
c represents the speed of propagation of the electro-magnetic-waves; 
T represents the (variable) period of the sawtooth signal. 
In addition to the above described elements, which ensure normal 
functioning of the prior art radar distance meter the feedback loop 
comprises an adder 9 included between the integrator 8 and the modulator 
2, and low-pass filter 10, which is arranged between the mixer stage 5 and 
the amplifier 7. The operation of these two additional elements will be 
explained hereinafter. For more detailed information of such a prior art 
distance measuring apparatus, reference is made to French Pat. No. 
1,557,670. 
The operation of the distance meter shown in FIG. 1 will be further 
explained with reference to FIG. 2. 
Let it first be assumed that the feedback loop at the output of the 
frequency discriminator 6 is interrupted. Then the modulator 2 produces an 
output voltage V.sub.m whose variation is shown by the curve a in FIG. 2a. 
This variation is assumed to be accurately linear. In response to this 
output voltage V.sub.m the high-frequency generator 1 produces a 
high-frequency output signal whose frequency variation is shown by the 
curve a in FIG. 2b. This last-mentioned curve is not linear and the 
deviation from the linearity may amount to some tens of percents at 
certain points. In response to the high-frequency signal generated by the 
high-frequency generator 1 an output voltage V.sub.d, whose variation is 
shown by the curve a in FIG. 2c is obtained at the output of the frequency 
discriminator 6. 
If now the feedback loop is closed, the output voltage V.sub.m of the 
modulator, the frequency F of the high-frequency generator and the output 
voltage V.sub.d of the frequency discriminator 6 will vary as indicated by 
the curves in the FIGS. 2a, 2b and 2c, respectively, the object being 
assumed to be punctiform. 
It appears that this feedback loop has a linearizing influence on the 
variation of the frequency of the high-frequency generator 1. This 
linearizing influence appears to depend on the response time of the 
feedback loop and is the more pronounced as the response time becomes 
shorter. The linearizing action thus obtained is, however, insufficient 
and the deviation of the linearity of the high-frequency generator 
frequency remains in the order of 27%, whereas a deviation of not more 
than 5% is acceptable. 
It appears, that the deviation from the actual variation of the frequency 
of the high-frequency generator and the linear variation thereof can be 
expressed mathematically with a reasonable approximation by the following 
equation: 
EQU .epsilon.(x)=2a x-3a x.sup.2 (2) 
wherein .epsilon. is the relative deviation from the desired slope and x is 
a normalized magnitude which is defined as follows: 
EQU x =T-.tau./T where O.ltoreq..tau..ltoreq.T 
Thus, the maximum deviation .DELTA..epsilon. between the strongest and the 
weakest slope is equal to: 
EQU .DELTA..epsilon.=.epsilon.(1/3)-.epsilon.(1)=4/3 
In expression 2 a=0.2 corresponds to the curve b shown in FIG. 2b for which 
it then holds that: 
EQU .DELTA..epsilon.=0.27. 
The large deviation of the linearity of the generator 1 results from the 
fact that the feedback loop has no store, so that this feedback loop for 
the linearizing operation recommences before each sawtooth and the time 
constant of this loop is not sufficiently small to obtain a sufficient 
linearization therein. 
As the above-described deviation of the linearity is systematic and changes 
only slowly, for example as a function of the temperature, each sawtooth 
period is divided into a predetermined number of time intervals, each 
having the same duration, and a number is alotted to each of these time 
intervals. A signal value which is representative of the deviation from 
the linearity occurring in that time interval is determined for each of 
these time intervals and these signal values are stored in a store and 
read in the time interval having the same number occurring in the next 
sawtooth period. The signal values thus obtained from the store are added 
in the adder 9 to the signal produced by the integrator 9 and the sum thus 
obtained controls the slope of the sawtooth voltage produced by the 
modulator 2. 
To that end the distance meter comprises a second feedback loop which, for 
the distance meter shown in FIG. 1, is of a digital implementation. 
Between the output of the frequency discriminator 6 and the second input 
of the adder 9, this digital loop comprises the cascade arrangement of a 
level detector 11, an adder 12, a store 13 and an digital-to-analog 
converter 14. The output of the store 13 is connected to a second input of 
the adder 12 by means of the conductor 15. A control device 16 is provided 
between the output of the modulator 2 and a control input of the store 13. 
Hereinafter the i.sup.th time interval of the p time intervals into which a 
period T of the sawtooth signal is divided, will be denoted by J.sub.i. At 
each time interval J.sub.i the control device reads a number M.sub.i from 
the store 13. 
The division of the sawtooth voltage V.sub.m into p time intervals J.sub.i 
is also performed by the control device 16, which for that purpose can be 
constructed in the manner shown in FIG. 3. The device of FIG. 3 comprises 
a comparator 20 to which the output signal of the modulator 2 is applied 
via a first input 21. The output of this comparator 20 is also the output 
of the control device. This output is further connected to the input of a 
modulo-p counter 22, whose output is connected to a digital-to-analog 
converter 23. The output of the converter 23 is connected to a second 
input 24 of the comparator 20. For the time the voltage at the input 21 is 
lower than the voltage at the input 24, the comparator 20 produces a first 
signal voltage. As soon as the voltage at the input 21 exceeds the voltage 
at the output 24 this comparator produces a second signal voltage in 
response to which the counting position of the counter 22 increases by one 
unit and, consequently, the output of the converter 23 by a calibrated 
voltage step .delta.V, in response to which the comparator 20 changes back 
to the first signal voltage, and remains in this position until the signal 
at the input 21 has increased by the value .delta.V. The control device 
thus produces a sequence of second signal voltages or pulses, namely a 
total of p within each period of the sawtooth voltage V.sub.m. As V.sub.m 
need not have an accurately linear variation, the output pulses of this 
control device do not appear with a fixed period, so that also the 
duration of the intervals J.sub.i may differ relative to one another. 
However, this phenomenon does not affect the proper operation of the 
distance meter. 
The store 13 may be in the form of a shift register consisting of p shift 
register sections, each being arranged for storing a k-bit word and whose 
content is shifted under the control of the pulses produced by the control 
device 16. Now the digital numbers M.sub.i which are coded with k bits 
appear at the output of this shift register, one of these k bits 
representing the sign bit of this number. In the time interval J.sub.i the 
number M.sub.i appearing at the output of the store 13 is applied to a 
digital-to-analog converter 14. The output signal of this converter 14 is 
added in the adder 9 to the output signal of the integrator 8 and the sum 
signal thus obtained controls the slope of the output signal of the 
modulator 2. The output voltage of the discriminator 6 produced during the 
time interval J.sub.i is applied to the level detector 11, which compares 
this output voltage with a positive as well as with a negative threshold 
voltage, whose absolute values are equal to one another. This detector 
produces a logic signal which is equal to +1, 0 or -1, respectively, 
depending on whether the input voltage is higher than the positive 
threshold voltage, is located between the two threshold voltages or is 
lower than the negative threshold voltage. These functions can be realized 
in known manner with two comparison devices. The output number, +1, 0 or 
-1 is algebraically added to the number M.sub.i by means of the adder 12 
and the result is again applied to the shift register (store). During the 
time interval J.sub.i+1 the store supplies the number M.sub.i+1 which, in 
like manner as M.sub.i, is increased or reduced by one unit or is kept 
constant. Finally, during the time interval J.sub.p the number M.sub.p 
appears at the output of the store. 
Level detector 11 is therefore a means for converting the analog signals 
from frequency discriminator 6 into three level signals that are 
integrated by a sampling type of digital integration constituted by adder 
12, store 13, digital-to-analog converter 14 and control device 16. Each 
time a pulse is generated by control device 16 the store 13 and adder 12 
add the +1, 0 or -1 signal from level detector 11 to the signal value in 
store 13, thus effecting a digital integration of the output from level 
detector 11. The sampling rate is set by control device 16 in response to 
the slope of the sawtooth wave from modulation 2 and increases in response 
to an increase in the sawtooth wave slope. 
Instead of being implemented as a shift register, the store 13 may 
alternatively be constituted by a storage medium, for example a RAM with 
addressable storage locations, it being possible to store one of the p 
numbers, consisting of k bits, in each of these storage locations. In that 
case the content of the modulo-p-counter 22 is applied as address code to 
the store 13, instead of the output pulses of the comparator 20 shown in 
FIG. 3. It will be apparent from the following example that the 
above-described measures have the desired effect. Starting from the 
expression for .epsilon.(x) in equation (2), then it holds that the change 
.delta..epsilon. of .epsilon.(x) is defined by the expression 
.delta..epsilon.=2a-6ax, so that at an interval of length p the average 
change of is equal to: 
EQU .delta..epsilon.=(2a-6ax)1/p 
The maximum value .vertline..delta..epsilon..vertline. occurring in the 
first time interval, notably for x=1, is equal to 4a/p. For a=0.2 and p=16 
it then holds that: 
EQU 4a/p=0-05 
which means in practice a 5% deviation from the linearity. 
FIGS. 4a-4c illustrate the effect of the digital feedback loop on the 
modulator 2 and the generator 1. Herein p is chosen equal to 8. More 
particularly, FIG. 4a represents the output voltage V.sub.m of the 
modulator 2. This curve, shown in FIG. 4a, is formed by means of 8 linear 
segments having a given slope, a discrete slope transient occurring at the 
transition from one segment to the other. 
FIG. 4b shows the variation of the frequency of the high-frequency 
generator in response to the output voltage, shown in FIG. 4a of the 
modulator. 
The deviation from the linearity .epsilon.(x) of the curve, shown in FIG. 
4b, is shown in FIG. 4c.