Capacitor amplifying circuit and operating method thereof

A capacitor amplifying circuit and an operating method thereof are disclosed. The capacitor amplifying circuit includes a first current source, a second current source, a current mirror unit, and an output capacitor. There is a proportion relationship between a first current of the first current source and a second current of the second current source. The current mirror unit is coupled between the first current source and the second current source. The current mirror unit includes N stages of current mirror circuit in series, wherein N is larger than or equal to 1. Each of the N stages of current mirror circuit has a proportional constant respectively. Two terminals of the output capacitor are coupled to the current mirror unit and a ground terminal respectively. The equivalent capacitance magnification of the output capacitor is related to the proportional constants based on the proportion relationship.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention relates to a capacitor amplifier; in particular, to a capacitor amplifying circuit capable of using a current mirror circuit to achieve a capacitor amplifying function without an operational amplifier and an operating method thereof.

2. Description of the Prior Art

In general, in an analog circuit, a capacitor amplifying circuit is often used to avoid the use of a capacitor having excessive capacitance value to properly reduce the area of the integrated circuit.

Please refer toFIG. 1.FIG. 1illustrates a schematic diagram of one type of conventional capacitor amplifying circuit. As shown inFIG. 1, the operational amplifier30is needed to be additionally disposed in the conventional capacitor amplifying circuit1used to compensate the frequency response of the amplifier20to make the capacitor22having small capacitance value C equivalent to a capacitor having large capacitance characteristics to achieve the capacitance compensation and amplification effect. However, the operational amplifier30additionally disposed in the conventional capacitor amplifying circuit1will increase cost and make the capacitor amplifying circuit1become more complicated.

Therefore, the invention provides a capacitor amplifying circuit and an operating method thereof to solve the above-mentioned problems occurred in the prior arts.

SUMMARY OF THE INVENTION

A scope of the invention is to provide a capacitor amplifying circuit. In a preferred embodiment, the capacitor amplifying circuit includes a first current source, a second current source, a current mirror unit, and an output capacitor. There is a proportion relationship between a first current of the first current source and a second current of the second current source. The current mirror unit is coupled between the first current source and the second current source. The current mirror unit includes N stages of current mirror circuit in series, wherein N is larger than or equal to 1. Each of the N stages of current mirror circuit has a proportional constant respectively. Two terminals of the output capacitor are coupled to the current mirror unit and a ground terminal respectively. The equivalent capacitance magnification of the output capacitor is related to the proportional constants based on the proportion relationship.

Another scope of the invention is to provide an operating method for a capacitor amplifying circuit. In a preferred embodiment, the capacitor amplifying circuit includes a first current source, a second current source, a current mirror unit, and an output capacitor. The operating method includes following steps of: (a) coupling the current mirror unit comprising N stages of current mirror circuit in series between the first current source and the second current source, wherein N is larger or equal to 1, each of the N stages of current mirror circuit has a proportional constant respectively; (b) coupling two terminals of the output capacitor to the current mirror unit and a ground terminal respectively; (c) using the first current source to provide a first current and using the second current source to provide a second current, wherein there is a proportion relationship between the first current and the second current; and (d) amplifying the output capacitor based on an equivalent capacitance magnification, wherein the equivalent capacitance magnification is related to the proportional constants based on the proportion relationship.

Compared to the prior arts, the capacitor amplifying circuit of the invention can use a current mirror circuit to amplify the capacitor having smaller capacitance value to make it equivalent to a capacitor having larger capacitance value without the operational amplifier additionally disposed in the conventional capacitor amplifying circuit. In addition, the capacitor and the current mirror circuit in the capacitor amplifying circuit of the invention are disposed between the two current sources, so that the manufacturing cost of the capacitor amplifying circuit will be reduced, and its circuit structure will become simpler and its size can be further shrunk to enhance the market competitiveness of the capacitor amplifying circuit.

The advantage and spirit of the invention may be understood by the following detailed descriptions together with the appended drawings.

DETAILED DESCRIPTION OF THE INVENTION

A preferred embodiment of the invention is a capacitor amplifying circuit. The capacitor amplifying circuit of the invention can be applied in an analog IC and used for compensating the frequency response of the amplifier, such as an error amplifier of a DC-DC converter, so that the amplifier can be operated at higher frequency to increase the bandwidth. In the preferred embodiment of the invention, it is not necessary to dispose additional amplifier in the capacitor amplifying circuit, the effect of capacitance equivalent compensation and amplification can be achieved by two preset fixed bias current sources, the current mirror principle, and the current operation of Kirchhoff voltage-current law (KCL/KVL).

Please refer toFIG. 2throughFIG. 4.FIG. 2illustrates a schematic diagram of a capacitor amplifying circuit not including any current mirror unit.FIG. 3illustrates an equivalent circuit diagram of the capacitor amplifying circuit inFIG. 2further including a current mirror unit.FIG. 4illustrates an embodiment of the capacitor amplifying circuit including a second stage of current mirror circuit.

As shown inFIG. 2, under the condition that the capacitor amplifying circuit does not include any current mirror unit, if the operational amplifier OA to be compensated is under a stable state, at this time, ΔI=0, the first current I1provided by the first current source41is equal to the second current I2provided by the second current source42, and the capacitance of the output capacitor43is C1. In this embodiment, the first current source41and the second current source42are preset fixed bias current sources, but not limited to this.

As shown inFIG. 3, the capacitor amplifying circuit4including the current mirror unit40is coupled to the output terminal of the operational amplifier OA to be compensated through a compensation resistor RCOMP, and at this time, the capacitance of the output capacitor43becomes C1′. In some implements, the capacitor amplifying circuit4can be directly coupled to the output terminal of the operational amplifier OA to be compensated without any specific limitations.

As shown inFIG. 4, the capacitor amplifying circuit4A includes the current mirror unit40, the first current source41, the second current source42, and the output capacitor43. In this embodiment, the first current source41and the second current source42are preset fixed bias current sources used for providing the fixed first current I1and the fixed second current I2respectively. The current mirror unit40includes two stages of current mirror circuit: the first stage of current mirror circuit CM1and the second stage of current mirror circuit CM2connected in series. In this embodiment, the first stage of current mirror circuit CM1is coupled to the output terminal of the operational amplifier OA to be compensated through a compensation resistor RCOMP, and the first stage of current mirror circuit CM1is coupled to the first current source41and the second current source42respectively. Two terminals of the output capacitor43are coupled to the ground terminal G and the node P between the first stage of current mirror circuit CM1and the first current source41respectively. In other embodiments, the first stage of current mirror circuit CM1can be directly coupled to the output terminal of the operational amplifier OA to be compensated; one terminal of the output capacitor43can be coupled to the node between the first stage of current mirror circuit CM1and the second current source42, but not limited to this.

In this embodiment, the first stage of current mirror circuit CM1includes a first switch T1and a second switch T2, and the gates of the first switch T1and the second switch T2are connected; the second stage of current mirror circuit CM2includes a third switch T3and a fourth switch T4, and the gates of the third switch T3and the fourth switch T4are connected. In practical applications, the first switch T1, the second switch T2, the third switch T3, and the fourth switch T4are transistors, such as P-MOSFET or N-MOSFET, but not limited to this.

The source and drain of the first switch T1of the first stage of current mirror circuit CM1are coupled to the first current source41and the second current source42respectively; the source and drain of the second switch T2are coupled to the third switch T3of the second stage of current mirror circuit CM2and the second current source42respectively; the fourth switch T4of the second stage of current mirror circuit CM2is coupled to the second current source42.

Capacitance means the ability (or capacity) of the capacitor to store charges. The amount of charge Q that the capacitor can store is proportional to its electric potential V, namely
Q=C*V(1)

Wherein, the proportional constant C in the formula (1) is the capacitance of the capacitor, referred to as the capacitance. In addition, the physical constant current formula is
I=Q/T(2)

Wherein, I is the current; Q is the amount of charge; T is the unit time. From the formulas (1) and (2), it can be obtained:
I*T=C*V(3)

In detail, the invention is based on the above-mentioned formulas (1), (2), and (3) and uses two preset fixed bias current sources and the current mirror proportional relationships based on Kirchhoff voltage-current law. It first establishes the DC bias current proportional relationship according to the set N current mirror proportional relationships, and the AC current will also comply with the DC current proportional relationship and use this relationship to achieve the capacitance compensation and amplification effect.

TakingFIG. 4for example, the first stage of current mirror circuit CM1and the second stage of current mirror circuit CM2have a first proportional constant K1and a second proportional constant K2respectively. That is to say, the first stage of current mirror circuit CM1having the first proportional constant K1means the proportion between the fixed first current I1flowing through the first switch T1and the current IK1flowing through the second switch T2is 1:K1; the second stage of current mirror circuit CM2having the second proportional constant K2means the proportion between the current IK1flowing through the third switch T3and the current IK2flowing through the fourth switch T4is 1:K2.

If the current mirror unit40including the first stage of current mirror circuit CM1and the second stage of current mirror circuit CM2and the operational amplifier OA to be compensated are all under the stable state, at this time, ΔI=0. According to Kirchhoff's Law, it can be obtained that:
I1+IK1+IK2=I2  (4)

According to the current mirror proportional relationship, it can be obtained that:
IK1=K1*I1  (5)
IK2=K2*IK1=K2*(K1*I1)  (6)

Putting the formulas (5) and (6) into the formula (4), it can be obtained that:
I2=I1*[1+K1*(1+K2)]
namely,I1=I2/[1+K1*(1+K2)]  (7)

From the formula (3), it can be obtained that under the same time T and the same capacitor electric potential V, the current I is proportional to the capacitance of the capacitor C. Therefore, from the formulas (3) and (7), it can be obtained that when the current mirror unit40includes the first stage of current mirror circuit CM1and the second stage of current mirror circuit CM2, the capacitance C1′ of the output capacitor43will be:
C1′=C1/[1+K1*(1+K2)]  (8)

The first current I1is equal to the second current I2under the condition without any current mirror unit shown inFIG. 2. The first current I1′ will become 1/[1+K1*(1+K2)] time of the first current I1ofFIG. 2under the condition that the current mirror unit40includes the first stage of current mirror circuit CM1and the second stage of current mirror circuit CM2shown inFIG. 4. Therefore, according to the formula (3), it can be found that under the condition shown inFIG. 4, the capacitance C1′ of the output capacitor43will become 1/[1+K1*(1+K2)] time of the capacitance C1of the output capacitor43shown inFIG. 2. It can be introduced as follows:

Under the condition without any current mirror unit shown inFIG. 2,
I1*T=C1*V(I1=I=2)  (9)

Under the condition that the current mirror unit40includes the first stage of current mirror circuit CM1and the second stage of current mirror circuit CM2shown inFIG. 4,
I1′*T=C1′*V
{I1/[1+K1*(1+K2)]}*T={1+K1*(1+K2)}*V
I1*T=C1*V(10)

From above, it can be found that the formula (9) is the same with the formula (10), that is to say, under the condition that the current mirror unit40includes the first stage of current mirror circuit CM1and the second stage of current mirror circuit CM2shown inFIG. 4, the current will become 1/[1+K1*(1+K2)] time of the current under the condition without any current mirror unit shown inFIG. 2, and its equivalent capacitance will also become 1/[1+K1*(1+K2)] time of the equivalent capacitance under the condition without any current mirror unit shown inFIG. 2. Therefore, as shown inFIG. 4, the capacitor amplifying circuit4A can equivalently amplify the smaller capacitance of the original output capacitor43[1+K1*(1+K2)] time through the first stage of current mirror circuit CM1and the second stage of current mirror circuit CM2of the current mirror unit40to achieve the capacitance compensation and amplification effect.

If taking practical data as example, if the first current I1=the second current I2=100 μA and the capacitance C1=100 pF inFIG. 2, the first proportional constant K1=the second proportional constant K2=10 inFIG. 4. If it is under the same unit time T and the capacitor electric potential V, it can be obtained by applying the formula (3) toFIG. 2:
100 μA*T=100 pF*V

Therefore, from above, it can be obtained that the capacitor amplifying circuit4A can equivalently amplify the smaller capacitance of the output capacitor43through the first stage of current mirror circuit CM1and the second stage of current mirror circuit CM2of the current mirror unit40to make it have the same effect with the larger capacitance of the output capacitor43under the condition without any current mirror unit shown inFIG. 2. And, the equivalent capacitance magnification of the output capacitor43is related to the first proportional constant K1of the first stage of current mirror circuit CM1and the second proportional constant K2of the second stage of current mirror circuit CM2in the current mirror unit40.

If taking the two stages of current mirror circuit (the first stage of current mirror circuit CM1and the second stage of current mirror circuit CM2) of the current mirror unit40as example, its equivalent capacitance is equal to C1*[1+K1*(1+K2)], that is to say, its equivalent capacitance magnification is [1+K1*(1+K2)]. Therefore, its equivalent capacitance magnification is related to the first proportional constant K1of the first stage of current mirror circuit CM1and the second proportional constant K2of the second stage of current mirror circuit CM2in the current mirror unit40.

Similarly, if taking the capacitor amplifying circuit4B inFIG. 5as example, its current mirror unit40includes N stages of current mirror circuit, for example, it includes three stages of current mirror circuit (the first stage of current mirror circuit CM1, the second stage of current mirror circuit CM2, and the third stage of current mirror circuit CM3), and N is any positive integer. From above, it can be found that its equivalent capacitance is equal to C1*[1+K1*(1+K2+K2*K3+K2*K3*K4+ . . . +K2*K3*K4* . . . *KN)], namely its equivalent capacitance magnification is [1+K1*(1+K2+K2*K3+K2*K3*K4+ . . . +K2*K3*K4* . . . *KN)]. Therefore, its equivalent capacitance magnification is related to the proportional constants K1˜KN of the N stages of current mirror circuit CM1˜CMN connected in series in the current mirror unit40.

In practical applications, one terminal of the output capacitor43can be not only coupled to the node P between the first stage of current mirror circuit CM1and the first current source41as shown inFIG. 4andFIG. 5, but also coupled to the node J between the first stage of current mirror circuit CM1and the second current source42as shown inFIG. 6andFIG. 7. If taking the capacitor amplifying circuit4C inFIG. 6as example, if the current mirror unit40including the first stage of current mirror circuit CM1and the second stage of current mirror circuit CM2and the operational amplifier OA to be compensated are all under the stable state, at this time, ΔI=0. According to Kirchhoff's Law, it can be obtained that:
I2=I1+IK1+IK2

Since the other derivation courses are similar to the above-mentioned embodiment, it does not further go into details. Finally, the result that its equivalent capacitance is equal to C1*[1+K1*(1+K2)] will be obtained.

If taking the capacitor amplifying circuit4D inFIG. 7as example, if the current mirror unit40including the first stage of current mirror circuit CM1through the fourth stage of current mirror circuit CM4and the operational amplifier OA to be compensated are all under the stable state, at this time, ΔI=0. According to Kirchhoff's Law, it can be obtained that:
I2=I1+IK1+IK2+IK3+IK4

Since the other derivation courses are similar to the above-mentioned embodiment, it does not further go into details. Finally, the result that its equivalent capacitance is equal to C1*[1+K1*(1+K2+K2*K3+K2*K3*K4)] will be obtained.

Furthermore, as shown inFIG. 4, if the operational amplifier OA to be compensated is not under the stable state, at this time, it will have the source/sink functions of the output current source, and the current changing amount ΔI is not equal to 0. If the operational amplifier OA is under the source current condition, it can be obtained according to Kirchhoff's Law and the current mirror proportional relationships:
ΔI=gm*ΔV=ΔI1+ΔIK1+ΔIK2
ΔI1=ΔI*{1/[1+K1*(1+K2)]}
ΔIK1=ΔI*{K1/[1+K1*(1+K2)]}
ΔIK2=ΔI*{K1*K2/[1+K1*(1+K2)]}

Wherein, gm is the transconductance of the operational amplifier OA to be compensated; ΔV is the voltage variation generated when the operational amplifier OA sources current; ΔI is the current variation generated when the operational amplifier OA sources current; ΔI1is the current variation generated when the operational amplifier OA distributed on the current path the of first current I1sources current; ΔIK1is the current variation generated when the operational amplifier OA distributed on the current path the of current IK1sources current; ΔIK2is the current variation generated when the operational amplifier OA distributed on the current path the of current IK2sources current.

Because the small signal current variation on the output capacitor43is ΔI1, under the same unit time T and the same capacitor electric potential V, it can be obtained based on the formula (3) that the capacitance variation of the output capacitor43is in multiples of the current variation ΔI1, and its AC current equivalent result will be the same with the DC analysis capacitive equivalent amplification principle. This result can let the operational amplifier OA operated under higher frequency to increase the bandwidth. Similarly, the above-mentioned analysis can be also applied to the operational amplifier OA operated under the current draining state, and the result is the same.

Another embodiment of the invention is a capacitor amplifying circuit operating method. In this embodiment, the capacitor amplifying circuit includes a first current source, a second current source, a current mirror unit, and an output capacitor. Please refer toFIG. 8.FIG. 8illustrates a flowchart of the capacitor amplifying circuit operating method in this embodiment. As shown inFIG. 8, in the step S10, the method couples the current mirror unit including N stages of current mirror circuit in series between the first current source and the second current source, wherein N is larger or equal to 1, and each of the N stages of current mirror circuit has a proportional constant respectively.

For example, as shown inFIG. 4, if N is equal to 2, namely the current mirror unit40of the capacitor amplifying circuit4A includes two stages of current mirror circuit (the first stage of current mirror circuit CM1and the second stage of current mirror circuit CM2) connected in series. The method couples the first stage of current mirror circuit CM1of the current mirror unit40between the first current source41and the second current source42, and the first stage of current mirror circuit CM1and the second stage of current mirror circuit CM2have the first proportional constant K1and the second proportional constant K2respectively. That is to say, the first stage of current mirror circuit CM1having the first proportional constant K1means that the proportion between the fixed first current I1flowing through the first switch T1and the current IK1flowing through the second switch T2is 1:K1; the second stage of current mirror circuit CM2having the second proportional constant K2means the proportion between the current IK1flowing through the third switch T3and the current IK2flowing through the fourth switch T4is 1:K2.

In the step S12, the method couples two terminals of the output capacitor to the current mirror unit and a ground terminal respectively. More detail, one terminal of the output capacitor43is coupled to the ground terminal G, and the other terminal of the output capacitor43can be coupled to the node P between the first stage of current mirror circuit CM1and the first current source41as shown inFIG. 4or to the node J between the first stage of current mirror circuit CM1and the second current source42as shown inFIG. 6.

In the step S14, the first current source provides a first current and the second current source provides a second current, wherein there is a proportion relationship between the first current and the second current. In fact, the first current source and the second current source are preset fixed bias current sources. For example, as shown inFIG. 4, the first current source41and the second current source42are preset fixed bias current sources for providing fixed first current I1and second current I2respectively. As to the proportional relationship between the first current I1and the second current I2, it can be determined based on practical needs without any specific limitations.

In the step S16, the method amplifies the output capacitor based on an equivalent capacitance magnification, wherein the equivalent capacitance magnification is related to the proportional constants based on the proportion relationship. Taking the two stages of current mirror circuit (the first stage of current mirror circuit CM1and the second stage of current mirror circuit CM2) of the current mirror unit40, it can be obtained based on the above-mentioned embodiments that its equivalent capacitance is equal to C1*[1+K1*(1+K2)], namely its equivalent capacitance magnification is equal to [1+K1*(1+K2)]. Therefore, it can be found that its equivalent capacitance magnification is related to the first proportional constant K1of the first stage of current mirror circuit CM1and the second proportional constant K2of the second stage of current mirror circuit CM2.

Compared to the prior arts, the capacitor amplifying circuit of the invention uses a current mirror circuit to compensate and amplify the capacitor having smaller capacitance value to make it equivalent to a capacitor having larger capacitance value without the operational amplifier additionally disposed in the conventional capacitor amplifying circuit. In addition, the capacitor and the current mirror circuit in the capacitor amplifying circuit of the invention are disposed between the two current sources, so that the manufacturing cost of the capacitor amplifying circuit will be reduced, and its circuit structure will become simpler and its size can be further shrunk to enhance the market competitiveness of the capacitor amplifying circuit.