JPH07115785A - Ultrasonic motor - Google Patents

Abstract

PURPOSE:To effectively drive an ultrasonic motor by reducing a starting current, decreasing starting current and suppressing heat generated from a driving circuit. CONSTITUTION:An inductance element 32 is connected in series with a plurality of electrodes disposed on the surface of a piezoelectric element for vibrating a vibration by generating mechanical vibration when alternating voltage is applied. The mechanical resonance frequency of a mechanical vibrating part is so set that X of an admittance Y=jx of a circuit in which an RLC series circuit of the part having an equivalent resistance of a resistance value Rm, an equivalent coil of a self-inductance Lm and an equivalent capacitor of an electrostatic capacity Cm is excluded from the equivalent circuit of an ultrasonic motor becomes a negative value.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an ultrasonic motor having ultrasonic vibration as a driving force, and more particularly to an ultrasonic motor having an electric resonance frequency and a mechanical resonance frequency adjusted.

[0002]

2. Description of the Related Art As a conventional technique which is the basis of the present invention, attention is paid to the self-capacitance of a vibrating body, an inductance element is connected in series or in parallel with this capacitance, and series resonance of this LC circuit is performed. Alternatively, there is provided an ultrasonic motor that utilizes parallel resonance and is optimized as a motor characteristic (Japanese Patent Laid-Open No. 4-281373).

An equivalent circuit of an ultrasonic motor in which inductance elements are connected in series is composed of an equivalent resistance having a resistance value R _m , an equivalent coil having an inductance L _m , and an equivalent capacitor having a capacitance C _m. R of mechanical vibration part
An LC series circuit, a capacitor having an intrinsic capacitance C _d connected in parallel to the RLC series circuit, and an inductance element having an inductance L _e connected in series to these.
It consists of In the ultrasonic motor configured as described above, the equivalent circuit constant R of the mechanical vibration of the ultrasonic motor is set so that the mechanical resonance frequency f _m and the electric resonance frequency f _e have the relationship of the following expression (1). The values of _m , L _m , C _m , the inductance _Le , and the intrinsic capacitance C _d are set. f _m ≤f _e (1) where f _m is the maximum value (the following formula (3)) of the absolute value | Y | (the following formula (2)) of the admittance Y of the RLC series circuit, _fe is obtained from the following equation (4).

[0004]

[Equation 1]

[0005]

[Equation 2]

[0006]

[Equation 3]

The equivalent circuit of the ultrasonic motor in which the inductance elements are connected in parallel is parallel to the RLC series circuit described above and the capacitor of the intrinsic capacitance C _d connected in parallel to the RLC series circuit. The configuration is such that an inductance element having an inductance L _p is connected. Also in the ultrasonic motor configured as above, the equivalent circuit constant R of the mechanical vibration of the ultrasonic motor is set so that the mechanical resonance frequency f _m and the electric resonance frequency f _e have the relationship of the following expression (5).
_m , L _m , C _m , inductance L _p , intrinsic capacitance C
The value of _d is set. f _m ≧ _fe (5) Here, f _m is obtained from the above equation (3), and _fe is obtained from the following equation (6).

[0008]

[Equation 4]

Further, the inductance element described above
Ultrasound connected in series or parallel or series and parallel
In the wave motor, mechanical vibration is generated from the equivalent circuit of the ultrasonic motor.
Admittance Y of the circuit excluding the RLC series circuit part
Is the equivalent circuit constant R such that_m, L_m,
C_mAnd inductance L_eAnd L_p, Intrinsic capacitance C _d
Is set. | 2Y / 2ω | ≧ 0 However, ω = 2πf ... (7)

[0010]

The frequency of the alternating voltage for driving the ultrasonic motor is changed from the frequency f _s higher than the mechanical resonance frequency f _m to the mechanical resonance frequency f.
The frequency is changed to around _m . Therefore, the ultrasonic motor in which the inductance elements are connected in series and has the relationship of the formula (1) is as shown in FIG. 4, and the ultrasonic motor in which the inductance elements are connected in parallel and has the relationship of the formula (5). As shown in FIG. 7, the motor consumes a large amount of power at the start of driving (frequency f _s ) and therefore overcurrent flows when the motor is started. Further, when the ultrasonic motor is continuously driven for a long time, the temperature of the piezoelectric ceramic, which is the material of the piezoelectric element, becomes high, and the electrostatic capacitance Cd between the electrodes becomes large. Therefore, the electric resonance frequency f _e ′ is calculated by the equation (4).
And becomes smaller than _{fe as} the value of C _{d in} equation (6) becomes larger. Therefore, the power consumption at the mechanical resonance frequency f _m becomes large as shown by the dotted lines in FIGS. 4 and 7.
Therefore, if the ultrasonic motor is continuously driven for a long time,
The power consumption increases, and the heat generated by the drive circuit also increases.

Further, regarding the frequency characteristics of the amplitude of the ultrasonic motor in which the inductance elements are connected in parallel, since the power supply voltage is directly applied to the motor, f _m ≤f _e , f _m ′ regardless of the inductance L _e. In either case of ≧ f _e, the same frequency characteristic is obtained. Therefore, it can be seen that shift width of the frequency for driving the ultrasonic motor are the same in either case of _{f m ≧ f e, f m} '≦ f e.

Further, in the case of an ultrasonic motor in which inductance elements are connected in series, an equivalent circuit of mechanical vibration of the ultrasonic motor is set so that the mechanical resonance frequency f _m is the same as the electric resonance frequency f _e. Setting the constants R _m , L _m , C _m , the inductance L _e , and the intrinsic capacitance C _d causes the following problems. That is, when the supplied voltage is V _i and the voltage between the electrodes is V ₀ , the voltage V ₀ between the electrodes is given by the following equation (8). V ₀ = V _i / (1-ω ² _Le C _d ) ... (8) Here, the mechanical resonance frequency f _m and the electric resonance frequency f _e
1-ω ² L _e in the above equation that the same bets (8)
Because C _d is 0, the value of the capacitance between the electrodes changes than the predetermined value C little by disturbances, comprising 1-ω ² L _e C _d is a positive or negative value. Therefore, when the value of the electrostatic capacitance between the electrodes becomes slightly larger than the predetermined value C, the voltage V ₀ between the electrodes becomes negative and the phase shifts by 180 ° with respect to the input voltage. When the value of the capacitance between the electrodes becomes smaller than the predetermined value C, the voltage V ₀ between the electrodes becomes positive and the phase difference becomes 0 with respect to the input voltage. Therefore, as shown in FIG. 9, when the ultrasonic motor is driven by applying a voltage shifted by 90 ° to the two electrodes of the A phase and the B phase, if the electrostatic capacitance C _d between the electrodes of the A phase is a little. However, when it becomes large, a voltage shifted by 180 ° with respect to the input voltage (phase 0 °) is applied. Further, when the value of the electrostatic capacitance C _d of the B phase becomes small as much as possible, the voltage of the same phase (90 °) is applied to the input voltage (the voltage shifted by 90 ° by the phase shifter). Therefore, the phase difference between the A phase and the B phase changes irregularly from 90 ° to −90 ° and does not function as a motor.

The admittance Y of the circuit excluding the RLC series circuit part of the mechanical vibration part from the equivalent circuit of the ultrasonic motor in which the inductance elements are connected in series or in parallel or in series and parallel is expressed by the above equation (7). Although the equivalent circuit constants R _m , L _m , C _m , the inductance L _e , and the specific capacitance C _d are set so that the above equation (7) takes the absolute value of the admittance, any admittance is obtained. The above expression (7) is satisfied.

The present invention has been made in view of the above facts, and an object of the present invention is to provide an ultrasonic motor capable of reliably driving by reducing the starting current, power consumption, and heat generation of the drive circuit. And

[0015]

To achieve the above object, the invention according to claim 1 is to provide a piezoelectric element or an electrostrictive element which generates mechanical vibration when an alternating voltage is supplied, and the piezoelectric element or the electrostrictive element. A vibrating body vibrated by mechanical vibration of, a plurality of electrodes arranged so that a plurality of alternating voltages having a predetermined phase difference can be applied to the piezoelectric element or the electrostrictive element, and each of the plurality of electrodes An inductance element connected in series, and an electrical resonance frequency determined by a capacitance between the electrodes and an inductance of the inductance element is set to be lower than a mechanical resonance frequency of the vibrating body. .

According to a second aspect of the present invention, a piezoelectric element or an electrostrictive element which generates mechanical vibration when an alternating voltage is supplied, and a vibrating body which is vibrated by the mechanical vibration of the piezoelectric element or electrostrictive element. A plurality of electrodes arranged so that a plurality of alternating voltages having a predetermined phase difference can be applied to the piezoelectric element or the electrostrictive element, and inductances connected in parallel between the corresponding electrodes of the plurality of electrodes. The electric resonance frequency determined by the element, the capacitance between the electrodes and the inductance of the inductance element is set to be higher than the mechanical resonance frequency of the vibrating body.

According to a third aspect of the present invention, a piezoelectric element or an electrostrictive element that generates mechanical vibration when an alternating voltage is supplied, and a vibrating body that is vibrated by the mechanical vibration of the piezoelectric element or electrostrictive element. Between a plurality of electrodes arranged so that a plurality of alternating voltages having a predetermined phase difference can be applied to the piezoelectric element or the electrostrictive element, and between electrodes corresponding to each of the plurality of electrodes in series or in the plurality of electrodes. Of each of the plurality of electrodes in series or in parallel with each of the plurality of electrodes connected in parallel between each corresponding electrode in the plurality of electrodes, and, from the equivalent circuit of the ultrasonic motor mechanical vibration part of The mechanical resonance frequency of the mechanical vibration part is set so that X in the admittance Y = jX (j is an imaginary unit) of the circuit excluding the RLC series circuit has a negative value. That.

[0018]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS A first embodiment of the present invention will be described below in detail with reference to the drawings. As shown in FIG. 1, the ultrasonic motor 80 of the present embodiment is provided with a ring-shaped vibrating body 82 made of copper alloy or the like, and a piezoelectric body 84 (see also FIG. 2) is attached to the vibrating body 82. A stator is formed. Piezoelectric body 8
Reference numeral 4 denotes a piezoelectric material that converts an electric signal into mechanical vibration, and is composed of a large number of electrodes that are divided and arranged in an annular shape. On the other hand, the rotor 86 attached to the drive shaft 85 is formed by adhering an annular slider 90 to a rotor ring 88 made of aluminum alloy or the like, and the slider 90 is brought into pressure contact with the vibrating body 82 by a spring 92. Has been done. As the slider 90, for example, engineering plastic or the like is used in order to obtain a stable friction force and a friction coefficient, which allows the rotor 86 to be driven with high efficiency. Then, to the piezoelectric body 84, the inductance elements 87 and 89 having the inductance L _e are connected in series (see also FIG. 2).

A drive circuit 94 as shown in FIG. 2 is connected to such an ultrasonic motor 80. That is, the drive circuit 94 includes an oscillator 96 including a voltage controlled oscillator (hereinafter referred to as VCO) and the like. A signal of a predetermined frequency output from the oscillator 96 is branched into two, one of which is amplified by the amplifier 98 and input to the piezoelectric body 84 via the inductance element 87 as a sin wave drive signal, and the other is phase shifter 100. Is input to the piezoelectric body 84 via the inductance element 89 as a cos wave drive signal after being amplified by the amplifier 102. Thus, the piezoelectric body 84 is excited by a standing wave of ultrasonic vibration due to the drive signal of the sin wave and a standing wave of ultrasonic vibration having a phase different from that of the vibration due to the drive signal of the cos wave. 82. By superimposing these two standing waves, the antinodes and nodes of the vibration are generated.
An ultrasonic vibration, which is a so-called traveling wave, that moves annularly along 2 is generated. This traveling wave is transmitted to the rotor 86, which is in pressure contact with the vibrating body 82, as a rotational force in a direction opposite to the traveling direction of the traveling wave, and the rotor 86 and the drive shaft 85 rotate.

The ultrasonic motor 80 described above is a two-phase drive, and the phase of the alternating voltage applied to each phase is the phase shifter 1.
Since there is no difference between the first and second phases other than the deviation of ± 90 ° at 00, only one phase will be described with reference to FIG. FIG. 3 shows an equivalent circuit for one phase of the ultrasonic motor. As shown in FIG. 3, the equivalent circuit for one phase of the ultrasonic motor has an equivalent resistance 22 of a resistance value R _m ,
Equivalent coil 24 of inductance L _m and capacitance C _m
R of the mechanical vibration part composed of the equivalent capacitor 26 of
LC series circuit, capacitor 28 of intrinsic capacitance C _d of the vibrator connected in parallel to this RLC series circuit, and RL
The C series circuit and the capacitor 28 are connected in series with the inductance element 32 having an inductance L _e . The equivalent circuit of the ultrasonic motor is connected to the power supply voltage via the amplifier 98.

In this embodiment, the equivalent circuit constant R _m of the mechanical vibration of the ultrasonic wave motor is set so that the mechanical resonance frequency f _m and the electric resonance frequency f _e have the relationship of the following expression (9). L
_m , C _m , the inductance _Le , and the intrinsic capacitance C _d are set so that the overall admittance has the frequency characteristic shown in FIG. f _m > _fe (9) The power consumption of the ultrasonic motor of the present embodiment is admittance |
Since Y | is multiplied by the square of the voltage, the result is as shown in FIG. Here, the frequency characteristic of admittance is f _m
Comparing the power consumption (FIG. 4) of the conventional ultrasonic motor having the relationship of ≦ f _{e with} the power consumption (FIG. 5) of the present embodiment, the total power from the start of driving the ultrasonic motor to the end thereof is Regarding the power consumption, in this embodiment, the power consumption at the start of driving is W ₁ ′, and the power consumption near the mechanical resonance frequency f _m that is continuously driven is W ₃ ′. On the other hand, in the conventional technique, the power consumption at the start of driving is W ₁ , and the power consumption near the mechanical resonance frequency f _m that is continuously driven is W _{1.
Is 3} . Therefore, as understood from FIGS. 4 and 5, the power consumption of the present embodiment is lower than that of the conventional technique. The power consumption at the start of driving the ultrasonic motor of this embodiment is W ₁ ′. This power consumption W ₁ ′
Is smaller than the power consumption W ₃ ′ for continuous driving,
Overcurrent does not flow at the start of driving the ultrasonic motor. Further, when the ultrasonic motor is continuously driven in the vicinity of the mechanical resonance frequency f _m , the electric resonance frequency f _e ′ becomes smaller than f _e as described above. Therefore, in the conventional technique in which the admittance has the frequency characteristic shown in FIG. 4,
Power consumption increases near the mechanical resonance frequency f _m (W
₂ > W ₃ ). On the other hand, in this embodiment, since the admittance has the frequency characteristic shown in FIG. 5, the mechanical resonance frequency f
_The power consumption near _m becomes small (W ₂ ′ <W ₃ ′). Therefore, as compared with the conventional technique, the circuit current of the drive circuit is reduced and the heat generation of the drive circuit can be suppressed.

Next, a second embodiment of the present invention will be described.
FIG. 6 shows an equivalent circuit of the ultrasonic motor of the second embodiment. As shown in FIG. 6, the equivalent circuit of the ultrasonic motor of the second embodiment has a configuration in which an inductance element 34 having an inductance L _p is connected in parallel to the RLC series circuit and the capacitor 28 described above.

In this embodiment, the equivalent circuit constant R _m of the mechanical vibration of the ultrasonic wave motor is set so that the mechanical resonance frequency f _m and the electric resonance frequency f _e have the relationship of the following expression (10).
L _m , C _m , inductance L _p , and intrinsic capacitance C _d are set so that the overall admittance has the frequency characteristic shown in FIG. _{f m <f e ···· (10} ) power consumption of the ultrasonic motor of the present embodiment, as shown in FIG. Here, the frequency characteristic of admittance is f _m ≤f
Comparing the power consumption of the conventional ultrasonic motor (FIG. 7) having the relationship of _{e with} the power consumption of this embodiment (FIG. 8), the total power consumption from the start of driving the ultrasonic motor to the end thereof In the present embodiment, the power consumption at the start of driving is W ₁ ′, and the power consumption near the mechanical resonance frequency f _m ′ that is continuously driven is W ₃ ′. On the other hand, in the related art, the power consumption at the start of driving is W ₁ , and the power consumption near the mechanical resonance frequency f _m that is continuously driven is W ₃ . Therefore, as understood from FIGS. 7 and 8, the power consumption of the present embodiment is lower than that of the conventional technique.
The power consumption at the start of driving the ultrasonic motor of this embodiment is W ₁ ′, and this power consumption W ₁ ′ is smaller than the power consumption W ₃ ′ at the time of continuous driving. No overcurrent flows at the start of driving. Further, when the ultrasonic motor is continuously driven in the vicinity of the mechanical resonance frequency f _m , the electric resonance frequency f _e ′ is as described above.
Is smaller than f _{e, the} power consumption near the mechanical resonance frequency f _m is large (W ₂ > W ₃ ) in the conventional technique in which the admittance has the frequency characteristic shown in FIG. 7.
On the other hand, in this embodiment, since the admittance has the frequency characteristic shown in FIG. 8, the power consumption near the mechanical resonance frequency f _m becomes small (W ₂ ′ <W ₃ ′). Therefore, compared with the conventional technique, in the present embodiment, the circuit current of the drive circuit is reduced, the drive efficiency is improved, and the heat generation of the drive circuit can be suppressed.

Next, the magnitude of the admittance Y of the circuit excluding the RLC series circuit part of the mechanical vibration part from the equivalent circuit of the ultrasonic motor in which the inductance elements are connected in series or in parallel or in series and parallel will be examined. This admittance Y is obtained by the following equation (11). However, j
Is an imaginary unit with j ² = −1. Y = jX (11) First, let us consider an admittance Y in which X in Expression (11) is X ≧ 0. The inductance Y of the ultrasonic motor in which the inductances are connected in series is obtained by the following equation (12). Y = j {(1 / ωC _d ) −ωL _e }, where ω = 2πf ... (12) where X ≧ 0, that is, (1 / ωC _d ) −ωL _e ≧
When set to 0, the following expression (13) is obtained. (2πf) ² ≦ 1 / (L _e C _d ) ... (13) The frequency f of the alternating voltage output from the oscillator is near the mechanical resonance frequency f _m , and the electric resonance frequency f Considering _e (equation (4)), the above equation (13) can be transformed into the following equation (14).

[0025]

[Equation 5]

Therefore, if X in the above formula (11) in the admittance Y of the circuit excluding the RLC series circuit part of the mechanical vibration part from the equivalent circuit of the ultrasonic motor is X ≦ 0, f
_It has a relationship of _m ≤ f _e .

The inductance Y of the ultrasonic motor in which the inductances are connected in parallel can be obtained by the following equation (15). Y = j {ωC _d −1 / (ωL _p )} However, ω = 2πf (15) where X ≧ 0, that is, ωC _d −1 / (ωL _p ) ≧
When set to 0, the relationship of the following expression (16) is obtained. (2πf) ² ≧ 1 / (L _e C _d ) ... (16) The frequency f of the alternating voltage output from the oscillator is in the vicinity of the mechanical resonance frequency f _m , and the electrical resonance frequency f Considering _e (formula (6)), formula (16) can be transformed into the following formula (17).

[0028]

[Equation 6]

Therefore, if X in the above equation (11) in admittance Y of the circuit excluding the RLC series circuit part of the mechanical vibration part from the equivalent circuit of the ultrasonic motor is X ≧ 0,
The relationship is f _m ≧ f _e .

From the above, when the equation (7) is a condition for the admittance Y, the relationship of f _m ≤f _e is established in the case of the ultrasonic motor in which the inductance elements are connected in series, but the inductance elements are connected in parallel. The relation of f _m ≧ f _e can be obtained for the ultrasonic motor thus manufactured, and the problems described in the problems to be solved by the invention arise.

Therefore, in the above-described first and second embodiments, it is assumed that X in the equation (11) is admittance Y having a negative value.

That is, in the case of the ultrasonic motor of the first embodiment, X <0, that is, (1 / ωC _d ) -ωL _e
When <0, the relationship of the following expression (18) is obtained.

[0033]

[Equation 7]

In the case of the ultrasonic motor of the second embodiment, X <0, that is, ωC _d −1 / (ωL _p ) <0.
Then, the relationship of the following expression (19) is obtained.

[0035]

[Equation 8]

From the above, X in the admittance Y (Equation (11)) of the circuit excluding the RLC series circuit part of the mechanical vibration part from the equivalent circuit of the ultrasonic motor in which the inductance elements are connected in series or in parallel is X <X. If it is 0, the relations of the equations (9) and (10) when the inductance elements are connected in series or in parallel are obtained.

The first embodiment and the second embodiment described above
In this embodiment, the mechanical resonance frequency f _mAnd electrical resonance frequency
Number f_eSo that the values of and are not the same.
Equivalent circuit constant R of mechanical vibration_m, L_m, C_mOr Indak
Closet L_e, Intrinsic capacitance C _dIs set,
The motor actually drives.

[0038]

As described above, according to the inventions of claims 1 to 3, according to the ultrasonic motor in which the inductance elements are connected in series or in parallel and in series and in parallel,
Since the electric resonance frequency and the mechanical resonance frequency are adjusted so as to reduce the power consumption, there is an excellent effect that an overcurrent does not flow during driving and the power consumption is reduced.

[Brief description of drawings]

FIG. 1 is a perspective view showing a schematic configuration of an ultrasonic motor.

FIG. 2 is a schematic configuration diagram of a drive circuit of an ultrasonic motor.

FIG. 3 is an equivalent circuit of the ultrasonic motor of the first embodiment in which inductance elements are connected in series.

FIG. 4 is a diagram showing frequency characteristics of admittance and power consumption of an equivalent circuit of a conventional ultrasonic motor having a mechanical resonance frequency smaller than an electrical resonance frequency.

FIG. 5 is a diagram showing frequency characteristics of admittance and power consumption of an equivalent circuit of the ultrasonic motor of the first embodiment having a mechanical resonance frequency higher than an electrical resonance frequency.

FIG. 6 is an equivalent circuit of the ultrasonic motor of the second embodiment in which inductance elements are connected in parallel.

FIG. 7 is a diagram showing frequency characteristics of admittance and power consumption of an equivalent circuit of a conventional ultrasonic motor having a mechanical resonance frequency smaller than an electrical resonance frequency.

FIG. 8 is a diagram showing frequency characteristics of admittance and power consumption of an equivalent circuit of the ultrasonic motor of the second embodiment having a mechanical resonance frequency higher than an electric resonance frequency.

FIG. 9 is a schematic configuration diagram of a drive circuit of an ultrasonic motor in which inductance elements are connected in series.

[Explanation of symbols]

 20 Ultrasonic motor equivalent circuit 32, 34 Inductance element

Claims (3)

[Claims] 1. A piezoelectric element or electrostrictive element that generates mechanical vibration when an alternating voltage is supplied, a vibrating body vibrated by mechanical vibration of the piezoelectric element or electrostrictive element, and the piezoelectric element or electric element. A plurality of electrodes arranged so that a plurality of alternating voltages having a predetermined phase difference can be applied to the strain element; and an inductance element connected in series to each of the plurality of electrodes; An ultrasonic motor in which an electric resonance frequency determined by a capacitance and an inductance of the inductance element is set to be lower than a mechanical resonance frequency of the vibrating body. 2. A piezoelectric element or electrostrictive element that generates mechanical vibration when an alternating voltage is supplied, a vibrating body vibrated by mechanical vibration of the piezoelectric element or electrostrictive element, and the piezoelectric element or electric element. A plurality of electrodes arranged so that a plurality of alternating voltages having a predetermined phase difference can be applied to the strain element, an inductance element connected in parallel to each of the corresponding electrodes in the plurality of electrodes, and between the electrodes An ultrasonic motor in which an electric resonance frequency determined by the electrostatic capacity of the element and the inductance of the inductance element is set to be higher than the mechanical resonance frequency of the vibrating body. 3. A piezoelectric element or an electrostrictive element that generates mechanical vibration when an alternating voltage is supplied, a vibrating body vibrated by mechanical vibration of the piezoelectric element or electrostrictive element, and the piezoelectric element or electric element. A plurality of electrodes arranged so that a plurality of alternating voltages having a predetermined phase difference can be applied to the strain element, and a plurality of electrodes arranged in series with each of the plurality of electrodes or in parallel between a plurality of electrodes corresponding to the plurality of electrodes. An inductance element connected in series to each of the electrodes and connected in parallel to each of the plurality of electrodes corresponding to each other, and an RL of a mechanical vibration part from an equivalent circuit of the ultrasonic motor.
An ultrasonic motor in which the mechanical resonance frequency of the mechanical vibration part is set such that X in the admittance Y = jX (j is an imaginary unit) of the circuit excluding the C series circuit has a negative value.