1. Field of the Invention
The invention relates to capacitance multiplier circuits. More particularly, the invention relates to tunable capacitance multiplier circuits.
2. Description of the Related Art
A phase-locked loop (PLL) is a circuit that generates a periodic output signal, or clock, that has a constant phase relationship with a periodic input signal. PLLs are closed loop frequency control systems whose operation depends on the detection of the phase difference between the input and output signals of the circuit, and which are used in many types of measurement, microprocessor and communication applications. Often, PLLs are used to generate clocks, or to recover clocks from received data in such applications.
Typically, a conventional PLL includes a phase/frequency detector (PFD), a charge pump, a loop filter, a voltage-controlled oscillator (VCO) to generate the PLL output clock, and a frequency divider. The PFD measures the difference in phase between an input clock and a feedback clock, which may be the PLL output clock itself, or a clock generated by passing the PLL output clock through the frequency divider, and generates an error signal that is proportional to the measured phase difference. The charge pump generates an amount of charge that is proportional to the error signal and inputs the charge to the loop filter. The loop filter outputs a VCO control voltage that is supplied to the VCO. The frequency of the PLL output clock generated by the VCO is controlled by the loop filter (VCO control) voltage supplied to the VCO.
In a PLL circuit, there are many applications where the loop bandwidth should be variable or changeable. Loop bandwidth is a characteristic of a PLL that limits the spectral response of a PLL. More specifically, loop bandwidth is the cutoff frequency in the frequency response of a PLL loop operation, indicating how fast the PLL loop response is.
One example in which the loop bandwidth should be variable is when a relatively wide loop bandwidth is needed for initial frequency acquisition (to reduce acquisition time) but a relatively narrow loop bandwidth is needed to achieve optimum noise performance after acquisition. Another example is a loop that tracks two or more signals having different spectral bandwidths. In this case, more than one PLL loop bandwidth may be required to optimize noise performance. In another example, it may be desirable to improve phase noise in one mode of operation and improve residual frequency modulation (FM) in a different mode of operation. Such improvements typically would need the loop bandwidth to be variable.
Conventionally, the loop bandwidth is set primarily by a single dominate capacitor that is part of the PLL loop filter. Conventional methods to change loop filter bandwidth include changing the phase detector charge pump current or changing the gain of the loop filter. In many cases, the use of a tunable capacitance multiplier circuit will address the issues described above. For example, a tunable capacitance multiplier circuit could replace the main loop filter capacitor with a variable capacitance, which in turn, could vary the loop bandwidth.
A capacitance multiplier circuit typically is a transistor or transistor circuit that is configured to multiply the value of a capacitor coupled to the base of the transistor by an amount equal to the transistor's gain, also known as beta (β). Conventionally, fixed (non-adjustable) capacitance multiplier circuits have been used in PLL applications.
One advantage of using a tunable capacitance multiplier circuit for the purpose of varying the PLL loop bandwidth is that relatively large values of capacitance can be realized using a relatively small physical capacitor. Capacitor value reduction of greater than ten times is not unreasonable. The ability to reduce the capacitor value is particularly important in integrated circuit applications where maximum on-chip capacitance values of 10 picofarads (pF) or less may require the use of a multiplier if the loop filter is to be included on the integrated circuit chip. Also, the ability to reduce the capacitor value can be important in very narrow-band loops where the loop capacitor value may be too large to be realized with a passive capacitor.
In the following description, like reference numerals indicate like components to enhance the understanding of the tunable capacitance multiplier circuits through the description of the drawings. Also, although specific features, configurations and arrangements are discussed hereinbelow, it should be understood that such specificity is for illustrative purposes only. A person skilled in the relevant art will recognize that other steps, configurations and arrangements are useful without departing from the spirit and scope of the invention.
The tunable capacitance multiplier circuits described herein involve the use of a network of multiple current sources to change or vary the capacitance value of the capacitance multiplier circuit. One or more of the current sources in the current source arrangement can be current mirrors or other suitable current sources. The tunable capacitance multiplier circuits are based on a current mirror design in which the capacitance value is adjustable. In PLL applications where the loop bandwidth is desired to be variable, the tunable capacitance multiplier circuit can replace the main loop filter capacitor to vary the loop bandwidth.
Referring now to
Referring now to
In the example, the current through the transistor Q1 (IC1) is 250 microamps (μA) and the current through the transistor Q2 (IC2) is K×IC1, or 4×250 μA=1 milliamp (mA). The equivalent multiplier capacitance is C1×(1+K)=0.066 μF×(1+4)=0.343 μF. The series resistance of the capacitance multiplier is 21 ohms. The value of the series resistance of the capacitance multiplier changes with the current through the transistor Q1. For example, when the current through the transistor Q1 changes from 500 VA to 125 μA, the series resistance of the capacitance multiplier changes from 10 ohms to 40 ohms, respectively. Also, the series resistance will be dependent on the characteristics of the transistors Q1 and Q2, although the given values are representative of what may be achieved typically. As discussed previously herein, PLL applications and other applications that desire a relatively low series resistance (i.e., a relatively high Q capacitor) may be negatively affected by the non-ideal model of the conventional capacitance multiplier circuit in
Referring now to
Each current source branch 38 includes a current source, CSN, having a corresponding gain KN. Each current source CSN can be any suitable current source arrangement. For example, one or more of the current sources CSN can be a current mirror arrangement using bipolar junction transistors or field effect transistors (FETs). Alternatively, one or more of the current sources CSN can be an operational amplifier (op-amp)-based current mirror arrangement, or other suitable current source or current source arrangement.
Each current source CSN is connected in series with a corresponding switch SN. Although each switch SN is shown as a physical switch, one or more of the switches SN can be any suitable switching arrangement, including switching arrangements that do not actually include a physical switch. For example, one or more of the switches SN can be a transistor switch.
In the manner shown, each current source CSN is switchably coupled between the input node 34 and the output node 36. That is, when the switch SN is closed, the corresponding current source CSN in the branch is coupled in parallel to the reference capacitor 32. When the switch SN is open, the corresponding current source CSN in the branch is not coupled to the reference capacitor 32. Therefore, each of the N current sources CSN can be selectively or switchably coupled to reference capacitor 32 depending on the state of its corresponding switch SN.
The current source branches 38 are switchably coupled to the reference capacitor 32 in such a way that the capacitance (CMULTIPLIER) of the tunable capacitance multiplier circuit 30, as measured across the input node 34 and the output node 36, is:
where CREF is the capacitance of the reference capacitor 32, Ki is the gain of the corresponding current source CSi relative to the current through the reference capacitor 32, and si is 1 if the switch Si is closed and 0 if the switch Si is open.
Depending on which current sources are switchably coupled to the reference capacitor 32, and depending on the gains K of the individual current sources, the capacitance of the multiplier circuit 30 can be controllably varied. For example, the values of the gain factors K for the individual current sources can be selected in a binary sequence. That is, K1=1, K2=2, K3=4, K4=8 and KN=2N−1. In such configuration, the capacitance of the multiplier circuit 30 would be variable between CREF and 15CREF, in equal steps of CREF, depending on which current sources are coupled to the reference capacitor 32.
For example, with four current source branches having gains according to above binary weighting scheme, if only the first and second current sources (CS1 and CS2) are coupled to the reference capacitor 32, the capacitance of the multiplier circuit 30 is 3CREF. (1CREF+2CREF). If only the first and third current sources (CS1 and CS3) are coupled to the reference capacitor 32, the capacitance of the multiplier circuit 30 is 5CREF(1CREF+4CREF). If only the first, second and fourth current sources (CS1, CS2 and CS4) are coupled to the reference capacitor 32, the capacitance of the multiplier circuit 30 is 11CREF (1CREF+2CREF+8CREF).
In another weighting scheme, the gains of the current sources are less than unity and decrease in a binary sequence. For example, K1=½, K2=¼, K3=⅛ and KN=½N. In such configuration, with four current source branches having gains according to a less than unity binary weighting scheme, the capacitance of the multiplier circuit 30 would be variable between CREF and 2CREF, in equal steps having a resolution of CREF/16. In yet another weighting scheme, the gains of the current sources are equal or approximately equal. In such configuration, with four current source branches having equal gains, the capacitance of the multiplier circuit 30 would be variable between CREF and 4CREF, in equal steps having a resolution of CREF.
As discussed previously herein, the tunable capacitance multiplier circuit 30 can be used in a PLL to vary the PLL loop bandwidth. The tunable capacitance multiplier circuit 30 allows relatively large values of capacitance to be realized using a relatively small physical capacitor. In many applications, this allows both the loop filter and the multiplier circuit to be included on the same integrated circuit chip. Also, being able to reduce capacitor value is important in very narrow-band loops where the loop capacitor value may be too large to be realized with a passive capacitor.
Referring now to
Typically, the loop filter 40 includes a first capacitor 46 (C1) connected in series with a parallel combination of a first or loop filter resistor 48 (R1) and a second capacitor 52 (C2), between the input node 42 and a point of reference potential, such as ground. Alternatively, although not shown, the loop filter can be a series combination resistor and capacitor, in parallel with a second capacitor, between the input node and ground. The loop filter also can include a second resistor 54 (R2) connected between the input node 42 and the output node 44, and a third capacitor 56 (C3) connected between the output node 44 and the point of reference potential.
In general, the phase/frequency detector generates an error signal, based on the difference between an input signal and a reference signal, and the charge pump generates an amount of charge proportional to the error signal. The loop filter accumulates the net charge from the charge pump and generates a loop filter voltage, which is input to the VCO as a control signal that biases the VCO. The VCO generates a periodic output signal, the frequency of which is a function of the loop filter voltage.
In a passive loop filter application, the first capacitor C1 creates a pole at close to zero frequency and is responsible for determining the gain of the loop filter. The loop bandwidth of the PLL is proportional to the square root of the gain of the loop filter, which is inversely proportional to the square root of the capacitance of the first capacitor C1. When using the passive loop filter, the loop bandwidth, ωn, is:
where C1 is the capacitance of the first capacitor C1 and KLoop is the PLL open loop gain excluding the loop filter.
The value of the first resistor R1 is selected to provide a zero that determines the phase margin or stability of the loop filter. The capacitors C2, C3 and the resistor R2 work together to provide high frequency poles that filter sampling spurs and frequencies much higher than the loop bandwidth. In many applications, it is possible to eliminate the second resistor R2 and the third capacitor C3 from the loop filter.
Since the first capacitor C1 determines the loop gain and therefore the loop bandwidth, the first capacitor C1 is an ideal candidate to be replaced with a tunable capacitance multiplier circuit, such as the conventional tunable capacitance multiplier circuit shown in
where R1bw1 and C1bw1 are the resistance and capacitance values, respectively, for the first loop bandwidth, and R1bw2 and C1bw2 are the resistance and capacitance values, respectively, for the second loop bandwidth. That is, the resistance of the first resistor R1 is inversely proportional to the square root of the capacitance of the first capacitor C1, if the phase margin stays the same. Also, the loop bandwidth is inversely proportional to the square root of the capacitance of the first capacitor C1. For the use of a tunable capacitance multiplier circuit in the loop filter 40 to be viable, a method for decreasing the resistance value of the first resistor R1 as the capacitance of the first capacitor C1 increases is needed. However, to maintain the same phase margin and to maintain loop stability, the product of the resistance of the resistor R1 times the square root of the capacitance of the capacitor C1 should be constant.
Referring now to
The variable loop bandwidth filter 60 also includes a tunable capacitance multiplier circuit 76, which, like the tunable capacitance multiplier circuit 30 shown in
To choose the resistance values for the first loop filter resistor 72 (R1a) and the second loop filter resistor 74 (R1b) such that the loop phase margin remains constant whether the switch 84 (S1) is open or closed:
where K is the gain factor of the current source 82 (CS), and R1 is the resistance value of the first resistor 48 (R1) in the loop filter circuit 40 in
As discussed hereinabove, in the variable loop bandwidth filter 60 in
Referring now to
In operation, the current source 82 senses the current through the reference capacitor 62 and multiplies that current by the current source gain factor K. Neglecting the second capacitor 66 (C2), when the switch 84 (S1) is closed, the impedance looking into the second loop filter resistor 74 (R1b) is made up of a capacitance (CREF×K) in series with a resistance (R1b/K). It is possible to select the values of the loop filter resistors R1a and R1b whereby the product of the sum of the resistances of R1a and R1b(R1a+R1b) times the square root of capacitance C1 of the reference capacitor 62 should be constant whether the switch 84 (S1) is opened or closed.
As the switch 84 (S1) is closed, the capacitance changes from CREF to K×CREF. Therefore, assuming the poles from the second capacitor 66 (C2), the second resistor 86 (R2) and the third capacitor 92 (C3) are large relative to the maximum loop bandwidth for the filter circuit 60, the loop bandwidth, ωn, is:
where C1 is the capacitance of the reference capacitor 62 (CREF) and KLoop is the PLL open loop gain excluding the loop filter. When the switch 84 (S1) is open, C1 is equal to CREF; when the switch 84 (S1) is closed, C1 is equal to CREF×K. Furthermore, the point of reference potential in a manner similar to the variable loop bandwidth filter 60. The variable loop bandwidth filter 100 also can include the second resistor 86 (R2) and the third capacitor 92 (C3) connected similar to that in the variable loop bandwidth filter 60.
However, in the variable loop bandwidth filter 100 in
The bias network 104 includes a transistor Q3, a transistor Q4, a transistor Q5, a voltage source V1 and a bias resistor Rbias connected together as shown. The transistors Q3 and Q4 are scaled in the same ratio as the transistors Q1 and Q2, i.e., the transistor Q4 is scaled in area to be K times the area of the transistor Q3. The bias network 104 is connected to the current mirror 102 and across the second loop filter resistor 74 (R1b) and the reference capacitor 62, as shown. The resistance value of the bias resistor Rbias determines the current through the transistor Q3, the transistor Q4, the transistor Q1 and the transistor Q2.
The variable loop bandwidth filter 100 is for use in PLL applications with two loop bandwidths. However, using a variety of current scaling constants, the variable loop bandwidth filter 100 also can be used in PLL applications with multiple bandwidths.
Also, the inventive variable capacitance multiplier circuits shown and described hereinabove are not limited to phase locked loop applications. Other applications in which this type of variable capacitance multiplier circuit may be useful include tunable filter applications where discrete frequency changes are sought, and VCO applications where discrete frequency steps are sought. Also, although the transistors shown and described herein are shown as bipolar junction transistors (BJTs), it should be understood that one or more of the transistors can be field effect transistors (FETs).
It will be apparent to those skilled in the art that many changes and substitutions can be made to the tunable capacitance multiplier circuits herein described without departing from the spirit and scope of the invention as defined by the appended claims and their full scope of equivalents.