1. A method of testing a frequency-dependent electrical circuit with input and output connections and of known component configuration, the method comprising the steps of:
(a) providing a circuit to be tested, the circuit having input and output connections;
(b) applying a.c. input test signals successively over a range of frequencies to the input connections of the circuit which is to be tested;
(c) measuring, at each frequency, the magnitude of the test signal across the input connections of the electrical circuit being tested;
(d) determining, from the magnitudes of the test signals at each of the range of frequencies, a tested frequency response of the circuit and identifying the shape of the characteristic frequency response for the known component configuration;
(e) comparing the shape of the characteristic frequency response to the tested frequency response;
(f) determining automatically, from the results of the frequency response comparison, whether the circuit is operational or faulty;
(g) determining, from the magnitudes of the test signals at each of the range of frequencies, the component values for an operational electrical circuit; and
(h) determining the insertion loss of the filter from the component values.
2. A method according to claim 1, wherein the circuit to be tested is a C-section filter.
3. A method according to claim 1, wherein the circuit to be tested is an L-section filter.
4. A method according to claim 1, wherein the circuit to be tested is a T-section filter.
5. A method according to claim 1, wherein the circuit to be tested is a pi-section filter.
6. A method according to claim 1, wherein the magnitude of the test signal is measured by taking the RMS voltage at the input connections.
7. A method according to claim 1, wherein the method of testing the circuit is fully automated using a-computer
8. A method of testing a C-section low pass filter, comprising the steps of:
(a) providing a C-section low pass filter as a circuit to be tested, the circuit having input and output connections;
(b) applying a.c. input test signals from a signal source successively over a range of frequencies to the input connections of the circuit which is to be tested;
(c) measuring, at each frequency, the magnitude of the test signal across the inputs of the C-section filter being tested;
(d) determining whether the C-section filter has a cut-off frequency in the range of test frequencies;
(e) estimating the resistance of a load applied to the outputs of the filter;
(f) using the cut-off frequency and the estimate of the load resistance to determine a value representing the total circuit capacitance for the operational C-section filter; and
(g) using the total circuit capacitance to determine the insertion loss of the filter.
9. A method of estimating the component values of an operational C-section low-pass filter having input and output connections, the output connections being connected to a load, comprising the steps of:
(a) providing a C-section low pass filter as a circuit to be tested, the circuit having input and output connections;
(b) applying a test signal from a signal generator to the input connections of the C-section filter with a known source resistance;
(c) varying the frequency of the test signal over a range of frequencies;
(d) measuring over the range of test frequencies the voltage developed across the input connections of the C-section filter and using the frequencies and associated voltages to form measured data pairs;
(e) estimating the resistance of the load applied to the filter, RL;
(f) estimating the 3 dB frequency, F3 dB, of the filter;
(g) calculating the effective circuit resistance, Rp, at the lowest frequency test signal from the relation:
23
R
P
=
R
L
R
S
R
L
+
R
S
;
(h) estimating the combined capacitance, CT, of the C-section filter capacitor and the load capacitor using the 3 dB frequency, F3 dB, and the effective circuit resistance, Rp, from the relation:
24
C
T
=
1
2
F
3
dB
R
P
;
and
(i) estimating the insertion loss, I, of the C-section filter at any given frequency using the estimated component values in the relation:
25
I
=
20
log
10
1
(
1
+
R
S
R
L
)
2
+
2
R
S
2
C
T
2
1
2
–
20
log
20
R
L
R
L
+
R
S
.
10. A method of estimating the component values of an operational C-section low-pass filter according to claim 9, wherein the step of estimating the resistance of the load resistance comprises estimating the load resistance RL using the relation:
26
R
L
=
R
S
V
low
V
oc
–
V
low
;
where Vlow is the voltage measured at the lowest frequency, and VOC is the open-circuit voltage.
11. A method of estimating the component values of an operational C-section low-pass filter according to claim 9, wherein the step of estimating the resistance of the load resistance comprises estimating the load resistance RL using the relation:
27
R
L
=
X
R
S
(
1
–
X
)
where
X
=
antilog
dB
low
20
and dBlow is the voltage ratio in decibels at a predetermined low frequency.
12. A method of estimating the component values of an operational L-section low-pass filter having input and output connections, the output being connected to a load, comprising the steps of:
(a) providing an L-section low pass filter as a circuit to be tested, the circuit having input and output connections;
(b) applying a test signal from a signal source input connections of the L-section filter with a known source resistance;
(c) varying the frequency of the test signal over a range of test frequencies;
(d) measuring over the range of test frequencies the voltage developed across the input connections of the L-section filter, and using the frequencies and associated voltages to form measured data pairs;
(e) estimating the load resistance, RL, of the load applied to the filter;
(f) estimating the 3 dB frequency, F3 dB, of the filter;
(g) making an initial estimate of the effective resistance, Rp, by assuming Re10 in the equation:
28
R
P
=
R
S
(
R
L
+
R
e1
)
R
S
+
R
L
+
R
e1
;
(h) making an initial estimate of the total capacitance, CT, using the initial estimate of Rp:
29
C
T
=
1
2
F
3
dB
R
P
;
(i) estimating the frequency fmin of an inflection point of the frequency response;
(j) making a first estimate of the resistance Re1 associated with inductor L1 at the minimum frequency in accordance with the equation:
30
R
e1
=
DR
S
1
–
D
where:
D
=
antilog
10
(
dB
at
f
min
20
)
;
(k) improving the estimate of the effective resistance, Rp, using the new value for Re1 in the equation in step (g); and (1) improving the estimate for CT from the equation in step (h).
13. A method of estimating the component values of an operational L-section low-pass filter according to claim 12, wherein the step of estimating the resistance of the load resistance comprises estimating the load resistance RL using the relation:
31
R
L
=
R
S
V
low
V
oc
–
V
low
;
where Vlow is the voltage measured at the lowest frequency, and VOC is the open-circuit voltage.
14. A method of estimating the component values of an operational L-section low-pass filter according to claim 12, is wherein the step of estimating the resistance of the load resistance comprises estimating the load resistance RL using the relation:
32
R
L
=
X
R
S
(
1
–
X
)
where
X
=
antilog
dB
low
20
and dBlow is the voltage ratio in decibels at a predetermined low frequency.
15. A method of estimating the component values of an operational L-section low-pass filter according to claim 12 including the step of using fmin to calculate the inductance, L1, in terms of the filter capacitance, C1:
33
L
1
=
1
(
2
)
2
(
f
min
)
2
C
1
.
16. A method of estimating the component values of an operational L-section low-pass filter according to claim 12 including the steps of:
(a) estimating
Z1Re1jL1
34
(
b
)
estimating
Z
3
=
1
j
C
1
estimating
ZLRL
(d) estimating the insertion loss of the filter, IL, from the filter components as:
35
I
L
=
20
log
10
Z
LZ
3
Z
LR
s
–
Z
LZ
1
+
Z
LZ
3
+
Z
3
R
S
+
Z
3
Z
1
–
20
log
10
Z
L
Z
L
+
R
S
.
17. A method of estimating the component values of an operational T-section low-pass filter comprising the steps of:
(a) providing a T-section low pass filter as a circuit to be tested, the circuit having input and output connections;
(b) applying a test signal from a signal source to the input connections of the T-section filter with a known source resistance;
(c) varying the frequency of the test signal over a range of test frequencies;
(d) measuring over the range of test frequencies the voltage developed across the inputs of the T-section filter, and using the frequencies and associated voltages to form measured data pairs;
(e) estimating the load resistance, RL, of the load applied to the filter;
(f) estimating the 3 dB frequency, F3 dB, of the filter;
(g) making an initial estimate of the effective resistance, Rp, by assuming Re1Re20 in the equation;
36
R
P
=
R
S
(
R
L
+
R
e1
+
R
e2
)
R
S
+
R
L
+
R
e1
+
R
e2
;
(h) making an initial estimate of the total capacitance, CT, using the initial estimate of Rp:
37
C
T
=
1
2
F
3
dB
R
P
;
(i) estimating the frequency fmin of the inflection point of the frequency response;
(j) making a first estimate of the resistance Re1 associated with inductor L1 at the minimum frequency fmin in accordance with the equation:
38
R
e1
=
D
R
S
1
–
D
where:
D
=
antilog
10
(
dB
at
f
min
20
)
;
(k) assuming that Re2Re1 and improving the estimate of the effective resistance, Rp, using the new value for Re1 and Re2 in the equation in step (g); and
(l) improving the estimate for CT from the equation in step (h).
18. A method of estimating the component values of an operational L-section low-pass filter according to claim 17, wherein the step of estimating the resistance of the load resistance comprises estimating the load resistance RL using the relation:
39
R
L
=
R
S
V
low
V
oc
–
V
low
;
where Vlow is the voltage measured at the lowest frequency, and VOC is the open-circuit voltage.
19. A method of estimating the component values of an operational T-section low-pass filter according to claim 17, wherein the step of estimating the resistance of the load resistance comprises estimating the load resistance RL using the relation:
40
R
L
=
X
R
S
(
1
–
X
)
where
X
=
antilog
dB
low
20
and dBlow is the voltage ratio in decibels at a predetermined low frequency.
20. A method of estimating the component values of an operational T-section low-pass filter according to claim 17, further comprising using fmin to calculate the inductance, L1, in terms of the filter capacitance, C1:
41
L
1
=
1
(
2
)
2
(
f
min
)
2
C
1
.
21. A method of estimating the component values of an operational T-section low-pass filter according to claim 20, including the steps of:
(a) estimating
Z1Re1jL1
(b) estimating
Z2Re2jL2
(c) estimating
42
Z
3
=
1
j
C
1
(d) estimating
ZLRL
(e) estimating the insertion loss of the filter, IL, from the filter components as:
43
I
L
=
20
log
Z
LZ
3
Z
2
R
S
+
Z
2
Z
1
+
Z
2
Z
3
+
Z
LR
S
–
Z
LZ
1
+
Z
LZ
3
+
Z
3
R
S
+
Z
3
Z
1
–
20
log
Z
L
Z
L
+
R
S
22. A method of estimating the component values of an operational pi-section filter having input and output connections, the output connections being connected to a load, comprising the steps of:
(a) providing a pi-section low pass filter as a circuit to be tested, the circuit having input and output connections;
(b) applying a series of test signals over a range of frequencies to the input connections of the pi-section filter;
(c) measuring for each of the range of test signal frequencies the voltage at the inputs of the pi-section filter, thereby obtaining voltagefrequency pairs;
(d) estimating the 3 dB frequency, F3 dB;
(e) estimating the load resistance RL of the filter;
(f) making a first estimate of the effective resistance Rp by setting Re0 in the following equation:
44
R
P
=
R
S
(
R
e
+
R
L
)
R
S
+
R
e
+
R
L
;
(g) making a first estimate of the total capacitance of the circuit, CT, using the relation:
45
C
T
=
1
2
F
3
dB
R
p
assuming that the capacitances of C1 and C2 are equal and thereby defining the total capacitance of the circuit, CT, as:
CTC1C2CLCL2C1
(h) determining the inflection points, the first inflection point being due to a minimum in the frequency response at fmin and the second inflection point being due to the maximum in the frequency response at fmax;
(i) estimating the frequency fb which defines a point on the frequency response of the pi-section filter where the voltage ratio of the measured voltage to the open circuit voltage is 3 dB less than the voltage ratio at the maximum frequency, fmax;
(j) extrapolating the initial slope of the frequency response to obtain an estimate of the frequency, fa, where the voltage ratio is also 3 dB below the voltage ratio at the maximum frequency, fmax;
fbF3 dB(lowVE);
(k) estimating the extrapolated frequency response, k, from frequencies fa and fb:
46
k
=
f
b
f
a
;
(l) obtaining a first estimate of C1-C2 using the estimate of CT from step (g) and the extrapolated frequency response k:
47
C
1
=
C
T
k
;
(m) improving the estimate of Re using the linear voltage ratio BVlowVOC, the estimates of RS and C1:
48
R
e
=
BR
s
(
(
1
–
B
)
2
–
B
2
2
C
1
2
R
s
2
)
1
2
where:
=
2
f
min
B
=
antilog
10
dB
‘
s
at
f
(
min
)
20
;
(n) replacing the estimate of Re with the new estimate from step (m) to obtain a further estimate of Rp;
(o) using the further estimate of Rp to find a further estimate of CT;
(p) using the further estimate of CT to find a further estimate of C1;
(q) repeating steps
(m) to
(p) until subsequent values of C1 are within a predetermined amount of each other.
23. A method of estimating the component values of an operational pi-section low-pass filter according to claim 17, wherein the step of estimating the resistance of the load is resistance comprises estimating the load resistance RL using the relation:
49
R
L
=
R
S
V
low
V
oc
–
V
low
;
where Vlow is the voltage measured at the lowest frequency, and VOC is the open-circuit voltage.
24. A method of estimating the component values of an operational pi-section low-pass filter according to claim 17,
wherein the step of estimating the resistance of the load resistance comprises estimating the load resistance RL using the relation:
50
R
L
=
X
R
s
(
1
–
X
)
where
X
=
antilog
dB
low
20
and dBlow is the voltage ratio in decibels at a predetermined low frequency.
25. A method of estimating the component values of an operational pi-section low-pass filter according to claim 17, further comprising the step of estimating the inductance of the filter using:
51
L
=
1
2
2
f
min
2
(
C
2
+
C
L
)
.
26. A method of estimating the component values of an operational pi-section filter according to claim 25, further comprising the steps of:
(a) estimating
52
Z
1
=
1
j
C
1
(b) estimating
Z2RejLe
(c) estimating
53
Z
3
=
1
j
(
C
L
+
C
2
)
(d) estimating
ZLRl
(e) estimating the insertion loss of the filter at any given frequency by substituting the component values into the relation:
54
I
L
=
20
log
10
Z
L
(
Z
1
2
Z
3
+
Z
1
Z
3
2
+
Z
1
Z
2
Z
3
P
where:
P
=
R
S
Z
1
2
Z
3
+
2
Z
1
Z
2
Z
3
+
Z
2
2
Z
3
+
Z
1
Z
3
2
+
Z
2
Z
3
2
+
R
S
Z
L
Z
1
2
+
2
Z
1
Z
2
+
2
Z
1
Z
3
+
Z
2
2
+
2
Z
2
Z
3
+
Z
3
2
+
Z
L
Z
1
2
Z
2
+
Z
1
Z
2
2
+
2
Z
1
Z
2
Z
3
+
Z
1
2
Z
3
+
Z
1
Z
3
2
+
Z
1
2
Z
2
Z
3
+
Z
1
Z
2
2
Z
3
+
Z
1
Z
2
Z
3
2
.
27. A method of estimating the component values of an operational pi-section filter having input and output connections, the output connections being connected to a load, comprising the steps of:
(a) providing a pi-section low pass filter as a circuit to be tested, the circuit having input and output connections;
(b) applying a series of test signals over a range of frequencies to the input connections of the pi-section filter;
(c) measuring for each of the range of test signal frequencies the voltage at the inputs of the pi-section filter, thereby obtaining voltagefrequency pairs;
(d) estimating the 3 dB frequency, F3 db;
(e) estimating the load resistance RL of the filter;
(f) making an estimate of the effective resistance Rp by setting Re0 in the following equation:
55
R
P
=
R
S
(
R
e
+
R
L
)
R
S
+
R
e
+
R
L
;
(g) making an estimate of the total capacitance of the circuit, CT, using the relation:
56
C
T
=
1
2
F
3
dB
R
p
assuming that the capacitances of C1 and C2 are equal and thereby defining the total capacitance of the circuit, CT, as:
CTC1C2CLCL2C1;
(h) determining the inflection points, the first inflection point being due to a minimum in the frequency response at fmin and the second inflection point being due to the maximum in the frequency response at fmax;
(i) estimating the frequency fb which defines a point on the frequency response of the pi-section filter where the voltage ratio of the measured voltage to the open circuit voltage is 3 dB less than the voltage ratio at the maximum frequency, fmax;
(j) extrapolating the initial slope of the frequency response to obtain an estimate of the frequency, fa, where the voltage ratio is also 3 dB below the voltage ratio at the maximum frequency, fmax:
fbf3 dB(VlowVE);
(k) estimating the extrapolated frequency response, k, from frequencies fa and fb:
57
k
=
f
b
f
a
;
and
(l) obtaining a first estimate of C1-C2 using the estimate of CT from step (g) and the extrapolated frequency response k:
58
C
1
=
C
T
k
.
28. A method of estimating the component values of an L-C filter, the filter output being connected to a load, comprising the steps of:
(a) providing a filter as a circuit to be tested, the circuit having input and output connections and containing at least one inductor and at least one capacitor;
(b) applying a test signal from a signal source input connections of the filter;
(c) varying the frequency of the test signal over a range of test frequencies;
(d) measuring over the range of test frequencies the voltage developed across the input connections of the filter, is and using the frequencies and associated voltages to form measured data pairs;
(e) estimating the load resistance, RL, of the load applied to the filter;
(f) making an initial estimate of the total effective circuit resistance, Rp;
(g) making an initial estimate of the total capacitance, CT;
(h) estimating the frequency fain of an inflection point of the frequency response;
(i) making a first estimate of the resistance Re associated with the inductor in the filter at the minimum frequency;
(j) iteratively improving the estimate of the effective resistance, Rp; and
(k) iteratively improving the estimate for CT.
29. A method of automatically verifying the characteristic frequency response of a low-pass filter having inputs and outputs, comprising the steps of:
(a) providing a low-pass filter to be tested, the filter having inputs;
(b) applying an a.c. test signal over a predetermined range of frequencies to the inputs of the filter;
(c) measuring for each of the frequencies the test voltage developed across the inputs of the filter;
(d) obtaining estimates of the open circuit voltage at one representative frequency or over the predetermined range of is frequencies;
(e) estimating the voltage ratio in dB of the test voltage to the open circuit voltage at each of the frequencies;
(f) associating the ratios in d with the particular frequency of the test signal and ordering the associated data by frequency;
(g) estimating the frequency at which the ratio is 3 dB less than the estimated voltage ratio at the lowest frequency;
(h) comparing the associated data at the 3 dB frequency with the next highest frequency data to determine whether the voltage ratio has decreased by an amount equivalent to less than 20 dB per decade;
(i) repeating step (h) with successive sets of associated data until the ratio has decreased by an amount equivalent to less than 20 dB per decade;
(j) continuing to step through the associated data until the ratio increases by an amount equivalent to less than 20 dB per decade;
(k) differencing the associated data and subtracting the mean value to form a set of differenced data;
(l) stepping through the differenced data and noting the first negative value and next subsequent positive value as the turning points of the frequency response.
30. A method of automatically verifying the characteristic frequency response of a low-pass filter having inputs and outputs according to claim 29, including the step of using the turning points of the frequency response to estimate the component values of the filter.
31. A method of automatically verifying the characteristic frequency response of a low-pass filter having inputs and outputs according to claim 29, in which steps (a) to (k) are fully automated using a microprocessor.
32. A method of automatically verifying the characteristic frequency response of a low-pass filter having inputs and outputs according to claim 29, including the step of interpolating between the associated data to estimate the frequency at which the ratio is 3 dB less than the estimated voltage ratio at the lowest frequency.
33. A method of automatically verifying the characteristic frequency response of a low-pass filter having inputs and outputs according to claim 29, wherein the a.c. test signal has a voltage less than 0.7 volts.
34. A method of automatically verifying the characteristic frequency response of a low-pass filter having inputs and outputs according to claim 29, wherein the step of differencing the data comprises determining the lowest frequency at which the difference value falls below the average of all the difference values.
35. A method of automatically verifying the characteristic frequency response of a low-pass filter having input and output connections according to claim 29, in which the associated data is differenced using a windowing technique.
36. Apparatus for testing a frequency-dependent electrical circuit with input and output connections and of known component configuration, the apparatus comprising:
(a) a signal source for applying a.c. input test signals successively over a range of frequencies to the input connections of a circuit which is to be tested;
(b) a meter for measuring, at each frequency, the magnitude of the test signal across the input connections of the electrical circuit being tested;
(c) means for determining, from the magnitudes of the test signals at each of the range of frequencies, a tested frequency response of the circuit and identifying the shape of the characteristic frequency response for the known component configuration;
(d) means for comparing the shape of the characteristic frequency response to the tested frequency response;
(e) means for determining automatically, from the results of the frequency response comparison, whether the circuit is operational or faulty;
(f) means for determining, from the magnitudes of the test signals at each of the range of frequencies, the component values for an operational electrical circuit; and
(g) means for determining the insertion loss of the filter from the component values.
37. Apparatus according to claim 36, wherein the meter measures the magnitude of the test signal by taking the RMS voltage at the input connections.
38. Apparatus according to claim 36, including a computer.
39. Apparatus for testing a C-section low pass filter, comprising:
(a) a signal source for applying a.c. input test signals successively over a range of frequencies to the input connections of the circuit which is to be tested;
(b) a meter for measuring, at each frequency, the magnitude of the test signal across the inputs of the C-section filter being tested;
(c) means for determining whether the C-section filter has a cut-off frequency in the range of test frequencies;
(d) means for estimating the resistance of a load applied to the outputs of the filter;
(e) means for using the cut-off frequency and the estimate of the load resistance to determine a value representing the total circuit capacitance for the operational C-section filter; and
(f) means for using the total circuit capacitance to determine the insertion loss of the filter.
40. Apparatus for estimating the component values of an operational C-section low-pass filter having input and output connections, the output connections being connected to a load, comprising:
(a) a signal source for applying a test signal from a signal generator to the input connections of the C-section filter with a known source resistance;
(b) means for varying the frequency of the test signal over a range of frequencies;
(c) a meter for measuring over the range of test frequencies the voltage developed across the input connections of the C-section filter and using the frequencies and associated voltages to form measured data pairs;
(d) means for estimating the resistance of the load applied to the filter, RL;
(e) means for estimating the 3 dB frequency, F3 dB, of the filter;
(f) means for calculating the effective circuit resistance, Rp, at the lowest frequency test signal from the relation:
59
R
P
=
R
L
R
S
R
L
+
R
S
;
(g) means for estimating the combined capacitance, CT, of the C-section filter capacitor and the load capacitor using the 3 dB frequency, F3 dB, and the effective circuit resistance, Rp, from the relation:
60
C
T
=
1
2
F
3
dB
R
P
;
and
(h) means for estimating the insertion loss, I, of the C-section filter at any given frequency using the estimated component values in the relation:
61
I
=
20
log
10
1
(
1
+
R
S
R
L
)
2
+
2
R
S
2
C
T
2
1
2
–
20
log
10
R
L
R
L
+
R
S
.
41. Apparatus for estimating the component values of an operational L-section low-pass filter having input and output connections, the output being connected to a load, comprising:
(a) a signal source for applying a test signal to input connections of the L-section filter with a known source resistance;
(b) means for varying the frequency of the test signal over a range of test frequencies;
(c) a meter for measuring over the range of test frequencies the voltage developed across the input connections of the L-section filter, and using the frequencies and associated voltages to form measured data pairs;
(d) means for estimating the load resistance, RL, of the load applied to the filter;
(e) means for estimating the 3 dB frequency, F3 dB, of the filter;
(f) means for making an initial estimate of the effective resistance, Rp, by assuming Re10 in the equation:
62
R
P
=
R
S
(
R
L
+
R
e1
)
R
S
+
R
L
+
R
e1
;
(g) means for making an initial estimate of the total capacitance, CT, using the initial estimate of Rp:
63
C
T
=
1
2
F
3
dB
R
P
;
(h) means for estimating the frequency fmin of an inflection point of the frequency response;
(i) means for making a first estimate of the resistance Re1 associated with inductor L1 at the minimum frequency in accordance with the equation:
64
R
e1
=
DR
S
1
–
D
where:
D
=
antilog
10
(
dB
at
f
min
20
)
;
(j) means for improving the estimate of the effective resistance, Rp, using the new value for Re1; and
(k) means for improving the estimate for CT.
42. Apparatus for estimating the component values of an operational L-section low-pass filter according to claim 41, including means for using fmin to calculate the inductance, L1, in terms of the filter capacitance, C1:
65
L
1
=
1
(
2
)
2
(
f
min
)
2
C
1
.
43. Apparatus for estimating the component values of an operational L-section low-pass filter according to claim 42, including means for:
(a) estimating
Z1Re1jL1
(b) estimating
66
Z
3
=
1
j
C
1
(c) estimating
ZLRL
(d) estimating the insertion loss of the filter, IL, from the filter components as:
67
I
L
=
20
log
10
Z
LZ
3
Z
LR
S
–
Z
LZ
1
+
Z
LZ
3
+
Z
3
R
S
+
Z
3
Z
1
–
20
log
10
Z
L
Z
L
+
R
S
.
44. Apparatus for estimating the component values of an operational T-section low-pass filter comprising:
(a) a signal source for applying a test signal to the input connections of the T-section filter with a known source resistance;
(b) means for varying the frequency of the test signal over a range of test frequencies;
(c) a meter for measuring over the range of test frequencies the voltage developed across the inputs of the T-section filter, and using the frequencies and associated voltages to form measured data pairs;
(d) means for estimating the load resistance, RL, of the load applied to the filter;
(e) means for estimating the 3 dB frequency, F3 dB, of the filter;
(f) means for making an initial estimate of the effective resistance, Rp, by assuming Re1Re20 in the equation;
68
R
P
=
R
S
(
R
L
+
R
e1
+
R
e2
)
R
S
+
R
L
+
R
e1
+
R
e2
;
(g) means for making an initial estimate of the total capacitance, CT, using the initial estimate of Rp:
69
C
T
=
1
2
F
3
dB
R
P
;
(h) means for estimating the frequency fmin of the inflection point of the frequency response;
(i) means for making a first estimate of the resistance Re1 associated with inductor L1 at the minimum frequency fmin in accordance with the equation:
70
R
e1
=
DR
S
1
–
D
where:
D
=
antilog
10
(
dB
at
f
min
20
)
;
(j) means for assuming that Re2Re1 and improving the estimate of the effective resistance, Rp, using the new value for Re1 and Re2; and
(k) means for improving the estimate for CT.
45. Apparatus for estimating the component values of an operational T-section low-pass filter according to claim 44, further comprising means for using fmin to calculate the inductance, L1, in terms of the filter capacitance, C1:
71
L
1
=
1
(
2
)
2
(
f
min
)
2
C
1
.
46. Apparatus for estimating the component values of an operational T-section low-pass filter according to claim 45, including means for:
(a) estimating
Z1Re1jL1
(b) estimating
Z2Re2jL2
(c) estimating
72
Z
3
=
1
j
C
1
(d) estimating
ZLRL
(e) estimating the insertion loss of the filter, IL, from the filter components as:
73
I
L
=
20
log
Z
LZ
3
Z
2
R
S
+
Z
2
Z
1
+
Z
2
Z
3
+
Z
LR
S
–
Z
LZ
1
+
Z
LZ
3
+
Z
3
R
S
+
Z
3
Z
1
–
20
log
Z
L
Z
L
+
R
S
47. Apparatus for estimating the component values of an operational pi-section filter having input and output connections, the output connections being connected to a load, comprising:
(a) a signal source for applying a series of test signals over a range of frequencies to the input connections of the pi-section filter;
(b) means for measuring for each of the range of test signal frequencies the voltage at the inputs of the pi-section filter, thereby obtaining voltagefrequency pairs;
(c) means for estimating the 3 dB frequency, F3 dB;
(d) means for estimating the load resistance RL of the filter;
(e) means for making a first estimate of the effective resistance Rp by setting Re0 in the following equation:
74
R
P
=
R
S
(
R
e
+
R
L
)
R
S
+
R
e
+
R
L
;
(f) means for making a first estimate of the total capacitance of the circuit, CT, using the relation:
75
C
T
=
1
2
F
2
dB
R
p
assuming that the capacitances of C1 and C2 are equal and thereby defining the total capacitance of the circuit, CT, as:
CTC1C2CLCL2C1
(g) means for determining the inflection points, the first inflection point being due to a minimum in the frequency response at fmin and the second inflection point being due to the maximum in the frequency response at fmax;
(h) means for estimating the frequency fb which defines a point on the frequency response of the pi-section filter where the voltage ratio of the measured voltage to the open circuit voltage is 3 dB less than the voltage ratio at the is maximum frequency, fmax;
(i) means for extrapolating the initial slope of the frequency response to obtain an estimate of the frequency, fa, where the voltage ratio is also 3 dB below the voltage ratio at the maximum frequency, fmax;
fbF3 dB(VlowVE);
(j) means for estimating the extrapolated frequency response, k, from frequencies fa and fb:
76
k
=
f
b
f
a
;
(k) means for obtaining a first estimate of C1-C2 using the estimate of CT and the extrapolated frequency response k:
77
C
1
=
C
T
k
;
(l) means for improving the estimate of Re using the linear voltage ratio BVlowVOC, the estimates of RS and C1:
78
R
e
=
BR
s
(
(
1
–
B
)
2
–
B
2
2
C
1
2
R
s
2
)
1
2
where:
=
2
f
min
B
=
antilog
10
dB
‘
s
at
f
(
min
)
20
;
(m) means for replacing the estimate of Re with the new estimate to obtain a further estimate of Rp;
(n) means for using the further estimate of Rp to find a further estimate of CT;
(o) means for using the further estimate of CT to find a further estimate of C1;
(p) means for iteratively repeating the above operation is until subsequent values of C1 are within a predetermined amount of each other.
48. Apparatus for estimating the component values of an operational pi-section low-pass filter according to claim 47, further comprising means for estimating the inductance of the filter using:
79
L
=
1
2
2
f
min
2
(
C
2
+
C
L
)
.
49. Apparatus for estimating the component values of an operational pi-section filter according to claim 48, further comprising means for:
(a) estimating
80
Z
1
=
1
j
C
1
(b) estimating
Z2RejLe
(c) estimating
81
Z
3
=
1
j
(
C
L
+
C
2
)
(d) estimating
ZLRL
(e) estimating the insertion loss of the filter at any given frequency by substituting the component values into the relation:
82
I
L
=
20
log
10
Z
L
(
Z
1
2
Z
3
+
Z
1
Z
3
2
+
Z
1
Z
2
Z
3
P
where:
P
=
R
S
Z
1
2
Z
3
+
2
Z
1
Z
2
Z
3
+
Z
2
2
Z
3
+
Z
1
Z
3
2
+
Z
2
Z
3
2
+
R
S
Z
L
Z
1
2
+
2
Z
1
Z
2
+
2
Z
1
Z
3
+
Z
2
2
+
2
Z
2
Z
3
+
Z
3
2
+
Z
L
Z
1
2
Z
2
+
Z
1
Z
2
2
+
2
Z
1
Z
2
Z
3
+
Z
1
2
Z
3
+
Z
1
Z
3
2
+
Z
1
2
Z
2
Z
3
+
Z
1
Z
2
2
Z
3
+
Z
1
Z
2
Z
3
2
.
50. Apparatus for estimating the component values of an operational pi-section filter having input and output connections, the output connections being connected to a load, comprising:
(a) a signal source-for applying a series of test signals over a range of frequencies to the input connections of a pi-section filter;
(b) means for measuring for each of the range of test signal frequencies the voltage at the inputs of the pi-section filter, thereby obtaining voltagefrequency pairs;
(c) means for estimating the 3 dB frequency, F3 dB;
(d) means for estimating the load resistance RL of the filter;
(e) means for making an estimate of the effective resistance Rp by setting Re0 in the following equation:
83
R
P
=
R
S
(
R
e
+
R
L
)
R
S
+
R
e
+
R
L
;
(f) means for making an estimate of the total capacitance of the circuit, CT, using the relation:
84
C
T
=
1
2
F
3
dB
R
p
assuming that the capacitances of C1 and C2 are equal and thereby defining the total capacitance of the circuit, CT, as:
CTC1C2CLCL2C1;
(g) means for determining the inflection points, the first inflection point being due to a minimum in the frequency response at fmin and the second inflection point being due to the maximum in the frequency response at fmax;
(h) means for estimating the frequency fb which defines a point on the frequency response of the pi-section filter where the voltage ratio of the measured voltage to the open circuit voltage is 3 dB less than the voltage ratio at the maximum frequency, fmax;
(i) means for extrapolating the initial slope of the frequency response to obtain an estimate of the frequency, fa, where the voltage ratio is also 3 dB below the voltage ratio is at the maximum frequency, fmax:
fbF3 dB(VlowVE);
(j) means for estimating the extrapolated frequency response, k, from frequencies fa and fb:
85
k
=
f
b
f
a
;
and
(k) means for obtaining a first estimate of C1-C2 using the estimate of CT and the extrapolated frequency response k:
86
C
1
=
C
T
k
.
51. Apparatus for estimating the component values of an L-C filter, the filter output being connected to a load, comprising:
(a) a signal source for applying a test signal to input connections of a filter;
(b) means for varying the frequency of the test signal over a range of test frequencies;
(c) a meter for measuring over the range of test frequencies the voltage developed across the input connections of the filter, and using the frequencies and associated voltages to form measured data pairs;
(d) means for estimating the load resistance, RL, of the load applied to the filter;
(e) means for making an initial estimate of the total effective circuit resistance, Rp;
(f) means for making an initial estimate of the total capacitance, CT;
(g) means for estimating the frequency fmin of an inflection point of the frequency response;
(h) means for making a first estimate of the resistance Re associated with the inductor in the filter at the minimum frequency;
(i) means for iteratively improving the estimate of the effective resistance, Rp; and
(j) means for iteratively improving the estimate for CT.
52. Apparatus for automatically verifying the characteristic frequency response of a low-pass filter having inputs and outputs, comprising:
(a) a signal source for applying an a.c. test signal over a predetermined range of frequencies to the inputs of a filter;
(b) a meter for measuring for each of the frequencies the test voltage developed across the inputs of the filter;
(c) means for obtaining estimates of the open circuit voltage at one representative frequency or over the predetermined range of frequencies;
(d) means for estimating the voltage ratio in dB of the test voltage to the open circuit voltage at each of the frequencies;
(e) means for associating the ratios in dB with the particular frequency of the test signal and ordering the associated data by frequency;
(f) means for estimating the frequency at which the ratio is 3 dB less than the estimated voltage ratio at the lowest frequency;
(g) means for comparing the associated data at the 3 dB frequency with the next highest frequency data to determine whether the voltage ratio has decreased by an amount equivalent to less than 20 dB per decade and for repeating the foregoing with successive sets of associated data until the ratio has decreased by an amount equivalent to less than 20 dB per decade;
(h) means for continuing to step through the associated data until the ratio increases by an amount equivalent to less than 20 dB per decade;
(i) means for differencing the associated data and subtracting the mean value to form a set of differenced data; and
(j) means for stepping through the differenced data and noting the first negative value and next subsequent positive value as the turning points of the frequency response.
The claims below are in addition to those above.
All refrences to claim(s) which appear below refer to the numbering after this setence.
What is claimed and desired to be secured by Letters Patent is:
1) A device for delivering energy stored in a spring moving between stressed and free states for the actuation of an auxiliary component, comprising:
(a) a housing including an inner cylindrical wall of a given diameter;
(b) a continuous length of compressible spring stored in said housing and positionable therein and along at least a portion of said wall in one of stressed and free states, said spring having an outer surface of a given diameter disposed along the continuous length thereof;
(c) means for selectively permitting movement of said spring from one of said stressed and free states to the other of said states within said housing; and
(d) dampening means for controlling the time for movement of said spring between said states and the actuation of said auxiliary component.
2) The device of claim 1: said dampening means comprising an elongated collar operatively positionable relative to said housing and including an inner wall along the elongate having first and second open ends and defining a restricted diameter passageway therethrough, the diameter of said restricted passageway being less than the diameter of the outer surface of said spring, whereby the outer surface of said spring frictionally engages the inner wall of said collar to delay movement of a length of said spring therethrough.
3) The device of claim 1: said dampening means comprising a diametrically restricted collar portion defined interiorly within said housing and further defining a restricted diameter passageway therethrough, the diameter of said restricted passageway being less than the diameter of the outer surface of said spring, whereby the outer surface of said spring frictionally engages the inner wall of said collar portion to delay movement of said length of spring therethrough.
4) The device of claim 1: said dampening means comprising a diametrically restricted collar portion defined interiorly within said housing and further defining a restricted diameter passageway therethrough, the diameter of said restricted passageway being less than the diameter of the outer surface of said spring, whereby the outer surface of said spring frictionally engages the inner wall of said collar portion to delay movement of said length of spring therethrough, said collar portion including at least one V-shaped series inner surface members, each member being angularly offset from the inner cylindrical wall of the housing.
5) A non-reusable retractable safety syringe comprising:
(a) a cylindrical barrel having first and second barrel ends and an inside diameter wall there between;
(b) a chamber for receipt of fluid within said barrel and between said first and second barrel ends;
(c) a plastic hollow plunger extendable into said barrel through the first end of said barrel, and selectively moveable from an expanded position toward an expended position immediate the second barrel end;
(d) a hollow needle in secured relationship relative to the second end of the barrel;
(e) spring biasing means including an outer surface, said spring biasing means being in initially secured relationship relative to the second end of the barrel for biasing the needle towards the hollow plunger;
(f) means for directing forward pressure upon said plunger to discharge fluid within said chamber and to actuate the spring biasing means to retract the hollow needle thereafter into the hollow plunger; and
(g) dampening means for controlling the time of effective movement of said spring biasing means as the hollow needle is moved into the cylindrical barrel.
6) The safety syringe of claim 5 wherein the dampening means comprises an elongated collar operatively positionable relative to said barrel and including an inner wall defining a restricted diameter passageway therethrough, the diameter of said restricted passageway being less than the diameter of the outer surface of said spring biasing means, whereby the outer surface of said spring biasing means frictionally engages an inner wall of said collar means to delay movement of said spring biasing means therethrough during activation of movement of said hollow needle toward said hollow plunger.