CA1093720A - Telephone range extender with gain - Google Patents

Abstract

TELEPHONE RANGE EXTENDER WITH GAIN
Abstract of the Disclosure The present invention relates to a telephone range extender. The extender is comprised of a unit for connecting the extender to a telephone central office and a unit for connecting the extender to a telephone subscriber loop. A subscriber loop resistance detector is connected to the subscriber loop connecting unit. A
negative impedance bilateral amplifier is connected in a configuration. The amplifier is comprised of a central office side shunt negative impedance converter, a series negative impedance converter and a subscriber side impedance transformer. Each of the negative impedance converters is adjustable in response to the subscriber loop resistance detector.

Description

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This is a division of Canadian patent application Serial No. 289,719 which was filed on 27 October 1977.
Back~und of the Invention l. Field of the Invention This invention relates to subscriber loop telephone service and, more particularly, to range extenders requiri.ng no adjustments for use with diverse subscriber loops.

2. Description of the Prior Art Range extenders for telephone loops are known by means of which the conventional telephone service is provided to sub-scribers over loops having lengths greatly in excess of normal telephone loops. This is accomplished by providing voice ~requency gain, sensitive detectors for off-hook and dialing currents, means for repeating the supervisory signals to the central office at increased current levels, and means for matching the impedance of long and sometimes loaded subscriber loops. Another use of range extenders is the substitution of higher gauge wire on subscriber loops, reducing the cost of the copper and ~ompensating for the higher resistance with the range extender. Prior art ran~e extenders are shown in J. L. Henry et al patent 3~508,009, granted April 2~ 1970, J. L. ~enry et al patent 3r671~676~ granted June 20, 1972, J. M. Nemchik patent 3,784,756, granted January 8, 1974, and H. W. Ott patent 4,004,102, granted January 8, 1977, all of which are U.S. patents.
These prior art range extenders have heretofore required manual ajustment of gain and/or impedance mat`ching character-istics in order to render them suitable or use with subscriber loops of varying lengths and wire gauge~ ~his requirement for manual adjustment increases the cost of installation and initial setup of such range extenders when moved from loop to 1GOP and, moreover, increases the risk of t?~

improper adjustment on a particular loop. The REG described in the above mentioned U.S~ patent of H. W. Ott, although it requires no manual adjustment of the impedance matching network, nevertheless includes a complicated and expensive impedance detecting circuit to control complex impedance matching networks. This complex circuitry increases the size and cost of the range extender, thereby reducing the number of loops over which this device can be used economically.
Since range extenders are sometimes used on subscriber loops of intermediate lengths, and since the range extender circuitry must go through many transient states while setting up and breaking down telephone calls, a danger exists of the negative impedance amplifier being in a high gain state during a transient condition when the central office termination presents an open circuit. Under these conditions the ampli-fier can become unstable and create oscillations or other undesirable transients which might interfere with normal telephone use.
Summary of the Invention In accordance with an aspect of the invention there is provided a telephone range extender comprising means for connecting said range extender to a telephone central office;
means for connecting said range extender to a telephone subscriber loop; a subscriber loop resistance detector connected to said subscriber loop connecting means; and a negative impedance bilateral amplifier connected in a ~
configuration, said amplifier comprising a central office side shunt negative impedance converter; a series negative impedance converter; and a subscriber side impedance transformer; each o said negative impedance converters being adjustable in response to said subscriber loop resistance detector.

In accordance with the illustrative embodiment of the present in~ention, the negative impedance amplifier is configured in the form of a ~ network having a negative impedance input shunt branch, a negative impedance serie~
branch, and an impedance transforming output shunt path.
Moreover, the frequency characteristics of both negative resistance converters and the impedance transformer are shaped so as to revert to positive impedance values in a controlled manner at the edges of the transmission band.
The ~ configuration provides a higher primary impedance for the transformer which couples to the subscriber loop.
The primary ampere turns of the transformer are correspond-ingly higher and can be used to buck out the loop ampere turns, resulting in a configuration that operates over a wide range of loop currents and yet without transformer saturation.
This permits the range extender to be used on relatively short loops. Moreover, the ~ configuration is less sensitive to component tolerances than other configurations since less use of bypass resistors is required to increase the current drawn from the central office.
One feature of the present invention is the exclusive use of normally-open rela~ contacts to control the gain of the negative impedance amplifier, thus permitting the use of miniaturized reed contacts with the resulting savings of power and costs in the range extender.
Another feature of the present invention is the placement of the loop impedance matching circuit (the line build-out network) on the primary side of the coupling transformer.
This allows the magnetic element of the network to be a simple coil rather than a three winding transformer. The impedance matching network interacts with the negative impedance amplifier charac~eris~ic so as to match any gauge q3~

of telephone cable over all expected varlations and in loop lengths.
Brlef Description of_the Drawing.
The present invention taken in conjunction with the invention disclosed in Canadian patent application Serial No~
289,719 filed 27 October 1977 will be described hereinbelow in detail with the aid of the accompanying drawing, in which:
FIG. 1 is a general block diagram of a range extender with gain having a ~ configured negative resistance amplifier in accordance with the present invention;
FIG. 2 is a detailed circuit diagram of the shunt negative impedance converter suitable for use in the range extender of FIG. l;
FIG. 3 is a detailed circuit diagram of a series negative impedance converter suitable for use in the negative impedance amplifier of FIG. l;
FIG. 4 is a detailed circuit diagram of a loop resistance detector suitable for use in the range extender of FIG. 1 for controlling the gain of the shunt and series negative impedance converters; and FIG. 5 is a circuit diagram of a dual mode current de~ector and logic circuit suitable for use in the range extender of FIG. 1.
Detailed Description Referring more particularly to FIG. 1/ there is shown a Range Extender with Gain (REG) connected to a telephone sub-scriber loop between the central office appearances 10 and the subscriber loop conductors 11. The ~EG of FIG. 1 comprises a negative impedance amplifier 15 including shunt negative impedance converter 12, series negative impedance converter 13, and transformer Tl. The negative impedance amplifier is separated from the central office lines 10 by a polarity ~3~7~
guard 14 including diodes CR7-10 and a surge protecting device CRll.
The negative impedance amplifier 15 is arranged in a ~ con-figuration and includes transformer Tl. The secondary wi~lings of trans-former Tl are connected through currerrt sensing resistors R46 and R49 in dual mode current detector 17 to subscriber loop conductors 11. A
bridge circuit 16 oomprising reciistors R38, R45, R47 and R48 is connected across sensing resistors R46 and R49 to provide a voltage to detec-tion circuits 33 in dual mode current detector 17 which is proE~ortional to the differential current flawing through resistors R46 a~l R49. The bridge arrangement provides a high impedance shunt to the subscriber loop and insures the cancellation of balanced longitudinal currents flow1ng through resistors R46 and R49.
Dual mode current detector 17 detects the current flowing in the subscriber loop to provide one input to the logic circuit 34 which, in turn, operates L relay 18 and RO relay 19. Detector 17 operates in one of two modes: a so-called t'slow mode" in which a low pass filter is introduced into the detection path to preJent the circuits from responding to ringing or other transient signals on the line. The operation of RO relay 19 causes detector 17 to shift to a so-called "fast mode" ~hich enables the accurate detection of dial pulses on loop 11. L relay 18 responds to these dial pulses by operating and releasing at a dial pulse rate.
When operated, L relay 18 closes L contacts 20 to connest resistor Rl across central office leads 10 and thus provide a shunt path to draw sufficient current from the central office battery to reliably operate the central office line relay. RO relay 19, when operated, connects the central office appearances 10 through the polarity guard 14, the negative impedance amplifier 15 i~; .

and transformer Tl to subscriber loop conductors 11, thus providing bilateral amplification of voice siynals therebetween. This amplifier connection is accomplished through RO transfer contacts 21, 22, 23l and 24.
A loop resistance detector 25 responds to the resistance of the connected loop 11 to operate AGC
relay 26 and adjust the gain of negative impedance amplifier 15. Thus AGC contacts 27 on shunt negative impedance converter 12 and ~GC contacts 28 on series negative impedance converter 28 modify the gain charac-teristics of these two negative impedance converters so as to provide an appropriate gain for the measured loop resistance. Loop resistance detector 25 is connected between the secondary windings of transformer T1 and also serves as a supply point for a talking batt~ry for loop 11. This battery has higher voltage than the normal central office talking battery, thus providing adequate telephone se-t transmitter current at extended loop ranges~
An optical isolator Vl comprising a light emitting diode and a phototransistor is used to detect breaks in the central office loop current which represent requests for tip party ground presence information to be used for Automatic Number Identification ~ANI). Isolator Vl is connected in series with the light emitting diode DSl, which serves as a panel light, and a current limiting resistor R71, across series negative impedance converter 13. Central office current from conductors 10 flows through the closed L and RO relay contacts 20 and 21 and the polarity guard 14. A portion of this central office current also flows through optical isolator Vl to provide a control signal on lead 30 to ~he logic

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circuit 34. Lead 30 is used to la~ch L relay 18 and to quickly release RO xelay 19 and thus provide a metallic path around amplifier 15 for performing a tip party ground test. AEter completion of the test, the signal on lead 30 changes state to permit ~O relay 19 to reoperate and L relay 18 to follow dial pulses and main-tain supervision.
An impedance matching network 31 comprising inductor Ll, shunted by resistor R70 and capacitor C35 and including capacitor C36, is interconnected with the primary winding of transformer Tl. Network 31 is used to provide an impedance match to loaded subscriber loops 11 of various lengths and wire gauge. In particular, the frequency characteristic of network 31, in combination with the frequency characteristics of the ~ network including negative impedance converters 12 and 13, pro-vide a reasonable impedance match over the entire voice frequency band and band edges for all 19 to 26 gauge, loaded t~lephone loops. More particularly, the combined impedance characteristics interact so as to match the negative impedance amplifier 15 to the loaded line împedance above 1 kHz and to decouple the line above 3.5 kHz. The fixed network 31 will match any fixed loading plan cable from 19 to 26 gauge satisfactorily.
It will be noted that only a single inductor Ll is required for this purpose, thus reducing the size and cost or the range extender in comparison to prior art extenders having buîld-out networks on the secondary side of the transformer and requiring more complex networks including more than one inductor and usually requiring manual adjustment for different loops.

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he operation of the range extender on both originating and terminatiny calls will now be described.
While the customer is still on-hook, the dual mode current detector 17 is operating in its slow mode and is monitoring the loop current. When the subscriber lifts the handset off the switchhook and thus completes the loop circuit, the resulting loop current is observed by detec-tor 17 0 After a slow mode delay o~ approximately 90 milliseconds, L relay 18 operates and then RO relay l9 operates. L relay 18 connects resistor Rl (approximately 1000 ohms) in shunt across the central office conductors lO. Current drawn by this shunt circuit and amplifier 15 when RO relay l9 operates causes the central office line relay to operate, thereby apprising the central office of the initiation of a callO
Shortly (lO milliseconds) after the operation of L relay 18, RO relay l9 operates to connect negative impedance amplifier 15 into the circuit and to change du~l mode detector 17 to its fast mode. Shunting resistor Rl is removed from the circuit and the input impedance of amplifier 15 substituted~ The input re-sistance of amplifier 15 is approximately the same value as resistor Rl (lOOO ohms). The central office line relay therefore continues to operate and hold. RO con~
tacts 23 and 24 also serve to connect a boosted talking battery in detector 25 to the subscriber loop, thereby increasing the current available to the subscriber telephone set.
At this point in the call, or at some latex point, a tip party ground test is required for two-party lines equipped with ANI circuitryO This is accomplished by interrupting the central office battery to remove 3i7~

loop current from conductors 10. This condition is de-tected-by optical isolator Vl and signalled to the logic circuit 34 via line 30. During the tip party ground test period, L relay 18 is held latched and RO relay 19 is released to permit the detection of longitudinal current in the subscr.iber loopO
When the tip party ground test is completed, central office battery is reconnected, this condition is detected by detector 17 and the RO relay 19 is reactivated.
The subscriber can then begin to dial, in-terrupting the loop current, and permitting detector 17 to detect the dial pulses. L relay 18 operates in respo.nse to detector 17 and repeats these dial pulses by operating L contacts 20. RO relay 19 remains operated throughout dial pulsing due to the slow release characteristic in the RO relay driver. Alternatively, TOUCHTONE ~ signals from a sub-scriber are amplified by amplifier lS and forwarded to the central office~
When tne called subscr~ber answers, amplifier 15 provides gain in both directio.ns to boost the range of such calls. When the calling subscriber hangs up, detector 17 detects the termination of loop current and releases L relay 18 and RO relay 19. L relay 18 releases almost immediately while RO relay 19 releases after a delay period of approximately 150 milliseconds. The range extender of FI~. 1 is now in its quiescent state watching for the appearance of loop current.
. On calls to the subscriber on loop 10, the central officQ applies 20 Hz ringing current to conductors 10. These signals are applied directly to loop conductors 11 through the normally closed portions _ 9 _ `T~ ~ ' ~ . -- '" .

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of RO contacts 22, 23, and 24. Detector 17 is not responsive to thes,e ringing signals due to its slow mode of response.
When the subscriber answers the telephone, the resulting loop current is detected by detector 17 to operate L relay 18 and thus shunt central office conductors 10 with resistor Rl. Shortly thereafter, RO relay 19 operates to connect negative impedance amplifier 15 into the loop and substitute the input impedance of the amplifier 15 for resistor Rl, The current drawn from the central ofice by resistor Rl or amplifier 15 operates the central office ring trip relay which then removes the ringing'signal from the line and completes the connection from the calling subscriber. L
relay 18 and RO relay 19 remain operated throughout the conversation to provide bilateral voice frequency gain with amplifier 15. When the subscriber on loop 11 hangs up, detector 17 detects this condi*ion as before and returns the range extender of FIG. 1 to its idle state.
Referring now to FIG. 2, there is shown a detailed circuit diagram of a shunt negative impedance converter suitable as converter 12 in FIG. 1. In general, the converter of FIG. 2 operates to change the positive resistance value of resistors R58, R59, and R60 into a negative value of approximately 1300 ohms which is shunted across the central office conductors 10. Resistors R52, R53, R54, and R55 serve to provide appropriate biasing levels for transistors Qll, Q12, Q13, and Q14. A frequency shaping network comprising resistors R56 and R57, and capacitor C29 serves to reduce the negative admittance of the negative impedance converter as frequency is increased~
This insures that the amplifier is s-table without oscillation outside of the voice frequency band and that the transition - 10 ~

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from the negative impedance characteristic to a positive impedance takes place in a gradual and controlled m~nner.
Capacitors C27 and C28 provide positive feedback from the collectors of transistors Q14 and Q12, respectively, to the base network of transistors Qll and Q13. This feedback directly causes the impedance inverslon of R58, RS9, and R60.
Transis-tor Qll drives transistor Q12 while transistor Q13 drives transistor Q14. The resulting negative impedance seen between terminals 50 and 51 is approximately 1300 ohms when AGC contact 12 is in its closed condition. This permits an overall gain of amplifier 15 (FIG. 1) of about 6 dB.
When AGC contact 27 is open, and resistor R60 and capacitor C30 are not shunting resistors R58 and R59, the negative impedance between terminals 50 and 51 increases to permit an amplifier gain of about 3 dB. Capacitor C30 prevents R60 from changing the dc biasing of converter 12 when AGC relay contact 27 is closed. Capacitors 27 and 23 roll off the negative admittance of the converter of FIG.
2 at the lower edge of the voice frequency bandO
It will be noted that only single normally open contact 27 is required to shift the negative impedance converter of FIG. 2. The AGC relay 26 (FIG. 1) can therefore be implemented with a miniaturized reed relay, thereby saving cost and power dissipation in the resulting range extender.
In FIG. 3 there is shown a series negative impedance converter which may be used for converter 13 in FIG. 1. The circuit of FIG. 3 operates to provide a negative series impedance between terminals 55 and 56.
Transistors QlS, Q16, Q17, and Q18 provide gain. The 30 resistance of resistors R64, R65, and R83 are converted into a negative impedance which is effectively connected .,, ";.

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~ in series with the loop conductors. This negative impedance ;, is modified below approximately 700 Hz by capacitor C31 to better match the low frequency characteristic of the connected cable without requiring a separate inductive network as is usually required. Resistors R62, R63, R66, R67, R68, and R69 serve to set the biasing levels for the various trans-istors and are powered directly from the connected telephone conductors. A resistor R61 is connected in series with the negative impedance converter to reduce the series negative impedance and thus reduce the amplifier gain to approximately 3 dB. When AGC relay 26 (FIG. 1) operates, AGC contact 28 operates to remove resistor R61 from the circuit, permitting the gain of the negative impedance amplifier to increase to 6 dB.
In general, the operation of AGC relay 26 results in a decrease in the magnitude of the shunt negative impedance and an increase in the magnitude of the series negative impedance. In combination, these changes change the gain of the overall amplifier 15 from 3 to 6 dB.
Referring to FIG. 4, there is shown a detailed circuit diagram of a loop resistance detector suitable for detector 25 in FIG. 1. As can be seen in FIG. 4, the subscriber loop is connected through transformer Tl to a boosted talking battery having a negative supply terminal 61 and a positive supply terminal 60. This voltage is applied from terminal 60 through voltage dropping resistor R73 and a thermistor RT3 to one secondary winding of transformer Tl. Similarly, terminal 61 is connected through matching resistor R72 and thermistor RT2 to the other secondary winding of transformer T2.
The positive temperature coefficients of RT2 and RT3 - 12 ~

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limit the loop current which can be drawn due to a loop fault (a short circuit; a ground, or a power cross) in the subscriber loop. Primary and secondary currents in transformer T1 are opposing so as to minimize the possibility of saturating the transformer on short, high current loops.
This permits the range extender to operate satisfactorily on shorter loops of approximately 1000 ohms while allowing use of a small, inexpensive transformer Tl.
Also connected between ~erminals 60 and 61 of the voltage supply is a voltage divider comprising resistors R74 and R75. The midpoint between resistors R74 and R75 is connected through resistor R76 to the positive input terminal of comparator 62. The midpoint of resistor R73 and thermistor RT3 is connected through resistor R77 to the negative input of comparator 62.
Capacitor C38 is connected between the positive and negative input terminals of comparator 62 and serve to delay the operation of comparator 62 until capacitor C38 is sufficiently charged.
The voltage drop across resistor R73 is compared in comparator 62 with the fixed threshold voltage across resistor R74 in comparator 62. If the signal at the negative input to comparator 62 .is more positive than the signal at the positive input terminal, comparator 62 produces a negative output voltage which is applied through resistor R79 to operate transistor Q19o Trans-istor Ql9, when ON, operates AGC relay 26 to set the gain of the amplifier ~5 :(FIG. 1) at 6 dB. When the negative input to comparator 62 is less than the positive input, comparator 62 produces a near zero voltage output which turns transistor Q19 off and releases AGC reiay 26, . ^,~
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~ returning amplifier 15 to a 3 dB gain condition.
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The detector of FIG. 4 switches the gain of amplifier 15 at about 2,000 ohms of loop resistance.
Resistor R78 around comparator 62 provides a positive feedback to eliminate indecision near the 2,000 ohm resistance point by effectively shifting the bridge balance point by 80 ohms equivalent loop resistance.
This is adequate to prevent indecision in the presence of up to 100 volts of 60 Hz longitudinally induced voltages on the loop.
A circuit path through diode CR13 and resistor R82 from lead 63 increases the threshold of comparator 62 to a sufficiently high level to force transistor Ql9 to the OFF state. This technique is used to insure that amplifier 15 of FIG. 1 is in the 3 dB gain state during dial pulsing and other transient conditions, as will be discussed in connection with FIG. 5. This increases the stability of the range extender during critical transient states when loop current is not detected.
In FIG. 5 there is shown a block diagram of a dual mode current detector and logic circuit suitable for current detector 17 and logic circuit 34 in FIG. 1.
This current detector and logic circuit is substantially identical to that shown in J.M. Nemchik patent 3,784,756, granted January 8, 1974, and hence will be described only in general terms here. The resistive bridge 16 o~ FIG. 1 is connected across capacitor Cl in FIG. 5 which, in : turn, is shunted by resistor R3, under the control of RO
transfer contacts 65. Capacitor Cl gives the current detector its slow mode characteristic by requiring capacitor Cl to charge before current can be detected.

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r When RO relay 19 operates, contacts 65 remove capacitorCl from,the circuit and cause it to be discharged through resistor R3, shiftiny the detector of FIG. 5 to its fast mode state.
A low-pass filter comprising resistors R28 and R29 and capacitors C20 and C21 prevent high frequency siynals from being coupled to the subscriber loop. A
high frequency oscillator 66 generates signals at a superaudible frequency (e.g., 18 kHz) which is supplied through capacitor C17 to diodes CR3 and CR4. A direct current flowing through diodes CR3 and CR4 varies the impedance of these diodes and thus the level of the high frequency signal transmitted therethrough. This high frequency is delivered by way of capaci-tor C16 through a high-pass filter 67 and a high freqùency amplifier 68 to peak-to-peak detector 69. .
The peak~to~peak voltage of the high frequency signal is an accurate measure of the direct current level in the subscriber loop. A pulse stretcher 70, having a preselected threshold, responds to the output of detector 69 to generate a 20 millisecond minimum pulse indicating the presence of a direct current signal in the subscriber loop exceeding the threshold. The output o~ pulse stretcher 70 is applied via lead 63 to the loop resistance detector of FIG. 4 to inhibit AGC relay 26 during intervals when loop current is not detected. This signal is also applied through OR gate 71 to energize driver 72 in order to operate L relay 18.
The output of pulse stretcher 70 is also applied directly to relay driver 73 to operate RO relay 19. Relay driver 73 has a slow release characteristic which can be overridden by a fast release signal on lead 74.
~ 15 -Flip-flop 75 is provided to latch relay 18 in the operated state and to hold relay lg in the unoperated state during tip par~y ground tests. Thus, the Q output of flip-flop 75 is applied through OR gate 71 and relay driver 72 to latch L relay 18. The same signal is applied through lead 74 to relay driver 73 to release RO relay 19.
Flip-flop 75 is set whenever loop current detector 17 is operated and an open circuit appears in the central office loop of the range extender. This open circuit is detected by the phototransis-tor in optical isolator Vl which ceases conductinc; when an open circuit occurs. This permits capacitor Cl9 to charge from the output of pulse stretcher 70 through resistor R21r Resistor R31 and normally closed contacts 76 prevent a charge from building up on capaci-tor Cl9 unless the negative impedance amplifier 15 (FIG. 1) is in the subscriber loop. When RQ relay 19 is released, capac-itor C19 is maintained in a discharge state preventing flip-flop 75 f-om being set.
In summary, then, flip-flop 75 can be set only if the following three conditions are present:
1. Pulse stretcher 70 is operatedr indicating the presence of subscriber loop current;
RO relay 19 is operated and the amplifier 15 is in the loop transmission path; and 3. The phototransistor in isolator Vl is off, indicating that the central office current has terminated in preparation to applying tip party ground test.
If all of these conditions are met, flip-flop 75 is set latching L relay 18 and releasing RO relay 19.

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The release of RO relay 19 releases RO contacts23 and.24 in FIG. 1 to remove battery from the local loop. Following the tip party ground tests, central office battery is reapplied to conductors 10, causing a current to flow in the subscriber loop. This current is detected by the current detector 17 of FIG. 5, resulting in the reoperation of pulse stretcher 70.
The leading edge of the output of pulse stretcher 70 is coupled through capacitor C23 to reset ANI flip-flop 75, thereby permitting RO relay 19 to operate and L relay 18 to track dial pulses.

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Claims (5)

The embodiments of the invention in which an exclusive property or privilege is claimed are defined as follows:

1. A telephone range extender comprising means for connecting said range extender to a telephone central office;
means for connecting said range extender to a telephone subscriber loop;
a subscriber loop resistance detector connected to said subscriber loop connecting means; and a negative impedance bilateral amplifier connected in a .pi. configuration, said amplifier comprising a central office side shunt negative impedance converter;
a series negative impedance converter; and a subscriber side impedance transformer;
each of said negative impedance converters being adjustable in response to said subscriber loop resistance detector.

2. The telephone range extender according to claim 1 wherein each said negative impedance converter includes a single normally open relay contact; and relay means for closing said normally open contacts in response to a preselected output level of said resistance detector.

3. The telephone range extender according to claim 1 wherein each of said negative impedance converters comprises a plurality of transistors connected in series with a positive impedance;
a voltage divider coupled to said subscriber loop for biasing said transistors from the direct current voltage on said subscriber loop; and means for changing the value of said positive impedance.

4. The telephone range extender according to claim 1 further including a passive fixed impedance matching circuit coupled to said .pi. configuration.

5. The telephone range extender according to claim 4 wherein the combination of the negative impedances of said converters and the positive impedances of said passive impedances is matched in the frequency domain to the impedance of said subscriber loop over a range of cable gauges and loop lengths without any adjustment of said passive impedances.