The disclosure relates in general to a frequency selective circuit.
In modern circuit designs, the frequency selective circuit, such as the low pass filter (LPF), is an indispensable block for filtering signals. For example, an inphase/quadrature modulator (IQM) may cooperate with a simple LPF cascaded by passive RC (resistor, capacitor) filters to generate signals to be transmitted. Once the frequency of unwanted signal is close to the desired signal, such LPF cannot provide enough rejections because of the low Q.
For getting better rejections, the designer needs to cascade more stages of RC filters, which occupied larger area, generates lager output noise and may corrupt the desired signal.
Therefore, there is a need of a frequency selective circuit capable of performing high Q filtering and reducing the output noise.
The disclosure is directed to a frequency selective circuit capable of performing high Q filtering and reducing the output noise.
According to one embodiment, a frequency selective circuit is provided. The frequency selective circuit includes a first transistor, an impedance element, a first capacitive element, a second capacitive element, a second capacitive and a second transistor. The first transistor includes a first terminal, a second terminal and a control terminal. The impedance element is coupled between the first terminal and the control terminal of the first transistor. The first capacitive element is coupled to the first terminal of the first transistor. The second capacitive element is coupled to the control terminal of the first transistor. The second transistor includes a first terminal, a second terminal and a control terminal, wherein the control terminal of the second transistor is coupled to the control terminal of the first transistor.
In the following detailed description, for purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding of the disclosed embodiments. It will be apparent, however, that one or more embodiments may be practiced without these specific details. In other instances, well-known structures and devices are schematically shown in order to simplify the drawing.
Below, exemplary embodiments will be described in detail with reference to accompanying drawings so as to be easily realized by a person having ordinary knowledge in the art. The inventive concept may be embodied in various forms without being limited to the exemplary embodiments set forth herein. Descriptions of well-known parts are omitted for clarity, and like reference numerals refer to like elements throughout.
The drain of the first transistor M1 is further coupled to the input current Ii, and thus a control voltage Vo is induced on the gate of the second transistor M2. In response to the control voltage Vo, the second transistor M2 generates the output current Io at its drain.
The transfer function of the frequency selective circuit 100 can be expressed as follows:
wherein H(s) represents the transfer function from the input current Ii to the output current Io, gm1 and gm2 represent the transconductances of the first and second transistors M1 and M2, respectively, C1 and C2 represent the capacitances of the first and second capacitive elements C1 and C2, respectively, and R1 represents the resistance of the resistor R1. According to equation eq1, the frequency selective circuit 100 can be regarded as a 2nd order current-mode filter. By appropriately selecting the values of the parameters shown in equation eq1, the Q-factor can be larger than 0.5. That is, the frequency selective circuit 100 is capable of perform a high Q filtering. Further, it can be obtained from
In some embodiments, the impedance element coupled to the first transistor may include at least one of a resistive element (e.g., a resistor) and an inductive element (e.g., an inductor).
In
wherein L1 represents the inductance of the inductor L1. As can be seen from equation eq2, the inductor L1 provides one more pole at frequency ωPL=R1/L1. Thus, the out-band rejections of the frequency selective circuit 200 can be further improved by appropriately choosing the pole frequency ωPL.
In some embodiments, the frequency selective circuit may cascade multiple sub-circuits to perform high-order filtering.
The simplified transfer function of the frequency selective circuit 400 can be expressed as follows:
wherein C3 to Cn respectively represent the capacitances of the capacitors C3 to Cn, and R2 to Rn-1 respectively represent the resistances of the resistors R2 to Rn-1.
The simplified transfer function of the frequency selective circuit 500 can be expressed as follows:
The transfer function of the frequency selective circuit 600 can be expressed as follows:
Compared to equation eq1, it can be obtained that the transfer function of the frequency selective circuit 600 remains the same. However, since the input swing can be determined by the transconductance of the third transistor M3, without affecting the designed frequency response, the third transistor M3 actually provides an extra degree of circuit design freedom, such that the low input swing design can be achieved.
The transfer function of the frequency selective circuit 700 can be expressed as follows:
wherein gm3 represents the transconductance of the third transistor M3. Compared to the previous embodiments, the frequency selective circuit 700 has more design freedom since the first and second capacitive elements C1 and C2 are isolated by the third transistor M3. Once the third transistor is biased at the linear region, the transfer function returns to eq1.
Due to the virtual short between the first and second inputs of the operational amplifier 802, the voltage at the node (i.e., source of the third transistor M3, or drain of the first transistor M1) coupling to the input current Ii is fixed and the input swing can be set to zero.
The impedance element ZA9 further includes a resistive element, e.g., the resistor R1, coupled between the drain and gate of the first complementary transistor MP1. The transfer function of the frequency selective circuit 900 can be expressed as follows:
wherein gM1 is the equivalent transconductance of the transconductances of the first complementary transistor Mp1 and the first transistor M1, and gM2 is the equivalent transconductance of the transconductances of the second complementary transistor Mp2 and the second transistor M2. Compared to the previous embodiments, the equivalent transconductances gM1 and gM2 are twice with the same current consumption.
The input differential pair 1002 includes two branches Bi1 and Bi2. The branch Bi1 includes a transistor M1p, a resistor R1P and a capacitor C2p. The drain of the transistor M1p is coupled to its gate via the resistor R1P, and the gate of the transistor M1P is further coupled to the capacitor C2p. Similarly, the branch Bi2 includes a transistor M1n, a resistor R1n and a capacitor C2n. The drain of the transistor M1n is coupled to its gate via the resistor R1n, and the gate of the transistor M1n is further coupled to the capacitor C2n. A capacitor C1′ is coupled between the drains of the transistors M1p and M1n.
The input differential pair 1002 can be regarded as a differential form of the left part of the frequency selective circuit 100 shown in
The output differential pair 1004 includes two branches Bo1 and Bo2. The branch Bo1 includes a transistor M2p to induce the output current Iop, and the branch Bo2 includes a transistor M2n to induce the output current Ion. Also, the output differential pair 1004 can be regarded as the differential form of the right part of the frequency selective circuit 100. In other words, the second transistor M2 can be used to form one branch Bo1/Bo2 of the output differential pair 1004, and the branch Bo1/Bo2 is coupled to the paired branch Bo2/Bo1 via the source of the second transistor M2.
The transfer function of the frequency selective circuit 1000 has the same form as that of the frequency selective circuit 100 shown in
In some embodiments, the source degeneration technique can be used to improve the linearity of the circuit. As shown in
If the term gm1R1>>1, equation eq8 can be simplified to
From equation eq9, it can be derived that the Q-factor is smaller than 0.5, which could not provide large rejection. In addition, for the frequency selective circuit 1300, the output noise induced by the resistor R1 is
Io=H(s)×(gm1+sC1)×√{square root over (4k′R1)} (eq10)
wherein k′ is a constant associated to temperature.
For comparison, it can be derived that the output noise induced by the resistor R1 of the frequency selective circuit 100 is expressed as follows:
Io=H(s)×sC1×√{square root over (4k′R1)} (eq11)
It can be found that the in-band output noise of the frequency selective circuit 100 is much smaller than that of the frequency selective circuit 1300, which proves that the proposed frequency selective circuit has better noise reduction performance.
The proposed frequency selective circuit can be used in various electronic devices.
In conventional passive-mixer based RX, the current-mode signal needs to be transferred to voltage domain by the TIA. In the embodiment, the CMF 1610 is placed before the TIA 1610, which relaxes the TIA design and improves the current consumption.
Based on the above, the present invention provides a frequency selective circuit which mainly includes a first transistor, an impedance element, a first capacitive element, a second capacitive element and a second transistor. The first transistor includes a first terminal (e.g., the drain/source), a second terminal (e.g., the source/drain) and a control terminal (e.g., the gate). The impedance element is coupled between the first terminal and the control terminal of the first transistor. The first capacitive element is coupled to the first terminal of the first transistor. The second capacitive element is coupled to the control terminal of the first transistor. The second transistor includes a first terminal, a second terminal and a control terminal coupled to the control terminal of the first transistor.
Due to the circuit configuration, the proposed frequency selective circuit exhibits excellent close-in rejections and noise performance. Further, the in-band roll-off of the proposed frequency can be much better than conventional cascaded RC LPF. In addition, the proposed frequency selective circuit needs not consume additional current, which is favored in low power design for portable design.
It will be apparent to those skilled in the art that various modifications and variations can be made to the disclosed embodiments. It is intended that the specification and examples be considered as exemplary only, with a true scope of the disclosure being indicated by the following claims and their equivalents.
This application claims the benefit of U.S. provisional Ser. No. 62/153,622, filed Apr. 28, 2015, the disclosure of which is incorporated by reference herein in its entirety.
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Number | Date | Country | |
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62153622 | Apr 2015 | US |