Resonator circuit

Abstract

A resonator circuit includes a transformer comprising a primary winding and a secondary winding. The primary winding is inductively coupled with the secondary winding. A primary capacitor is connected to the primary winding. The primary capacitor and the primary winding form a primary circuit. A secondary capacitor is connected to the secondary winding. The secondary capacitor and the secondary winding form a secondary circuit. The resonator circuit has a common mode resonance frequency at an excitation of the primary circuit in a common mode. The resonator circuit has a differential mode resonance frequency at an excitation of the primary circuit in a differential mode. The common mode resonance frequency is different from the differential mode resonance frequency.

Claims

1. A radio frequency oscillator, comprising: a first winding and a second winding; a first capacitor connected to two ends of the first winding; and a second capacitor connected to two ends of the second winding; wherein the first capacitor comprises a pair of single-ended capacitors, and wherein the second capacitor comprises a pair of differential capacitors; wherein the pair of single-ended capacitors are connected in series; wherein the radio frequency oscillator comprises a common mode resonant frequency and a differential mode resonant frequency; wherein the radio frequency oscillator further comprises an excitation circuit configured to excite the radio frequency oscillator in the common mode and in the differential mode; wherein the excitation circuit comprises a pair of transistors, and wherein a resistor is coupled to source terminals of the pair of transistors.

2. The radio frequency oscillator of claim 1, wherein the pair of differential capacitors are connected in series, and wherein the pair of single-ended capacitors are configured to provide a reference to ground potential.

3. The radio frequency oscillator of claim 2, wherein the pair of single-ended capacitors are configured to tune both the common mode resonant frequency and the differential mode resonant frequency; and wherein the pair of differential capacitors are configured to tune the differential mode resonant frequency.

4. The radio frequency oscillator of claim 1, wherein the resistor is tunable.

5. The radio frequency oscillator of claim 1, wherein the inductance associated with the first winding in the common mode is greater than the inductance associated with the first winding in the differential mode.

6. The radio frequency oscillator of claim 3, wherein the pair of single-ended capacitors comprise a first single-ended capacitor and a second single-ended capacitor; wherein a first end of the first single-ended capacitor is coupled to a first end of the first winding, and a second end of the first single-ended capacitor is coupled to a ground potential; wherein a first end of the second single-ended capacitor is coupled to a second end of the first winding, and a second end of the second single-ended capacitor is coupled to the ground potential.

7. The radio frequency oscillator of claim 6, wherein the pair of single-ended capacitors further comprise a first transistor and a second transistor; wherein the first transistor is configured to connect and disconnect the first single-ended capacitor between the first end of the first winding and the ground potential; wherein the second transistor is configured to connect and disconnect the second single-ended capacitor between a second end of the first winding and the ground potential.

8. The radio frequency oscillator of claim 7, wherein the gate of the first transistor and the gate of the second transistor are coupled to a same control signal from an inverter.

9. The radio frequency oscillator of claim 1, wherein the pair of differential capacitors comprise a first differential capacitor and a second differential capacitor.

10. The radio frequency oscillator of claim 9, wherein the first differential capacitor and the second differential capacitor are a pair of balanced capacitors.

11. The radio frequency oscillator of claim 10, further comprising: a switch coupled between the first differential capacitor and the second differential capacitor, wherein the switch is configured to connect and disconnect the first differential capacitor and the second differential capacitor to and from one another.

12. The radio frequency oscillator of claim 1, wherein the pair of differential capacitors comprises a plurality of switched capacitors configurable to be arranged in parallel.

13. The radio frequency oscillator of claim 1, wherein the common mode resonant frequency of the radio frequency oscillator is independent from the second capacitor, and the differential mode resonant frequency of the radio frequency oscillator is dependent on the second capacitor.

14. A method for tuning a radio frequency oscillator, comprising: coupling two ends of a first winding to a first capacitor, wherein the first capacitor comprises a pair of single-ended capacitors, wherein the pair of single-ended capacitors are connected in series; coupling two ends of a second winding to a second capacitor, wherein the second capacitor comprises a pair of differential capacitors; exciting, by a pair of transistors, the radio frequency oscillator in a common mode and in a differential mode; and coupling a resistor to a source terminal of the pair of transistors.

15. The method of claim 14, further comprising: coupling the pair of differential capacitors in series; providing a ground potential as a reference to the pair of single-ended capacitors; tuning, by the pair of single-ended capacitors, both a common mode resonant frequency of the radio frequency oscillator and a differential mode resonant frequency of the radio frequency oscillator; and tuning, by the pair of differential capacitors, the differential mode resonant frequency of the radio frequency oscillator.

16. The method of claim 15, wherein the pair of single-ended capacitors comprise a first single-ended capacitor and a second single-ended capacitor, and wherein the pair of single-ended capacitors further comprise a first transistor and a second transistor; wherein the method further comprises: coupling a first end of the first single-ended capacitor to a first end of the first winding, coupling a second end of the first single-ended capacitor to a ground potential; coupling a first end of the second single-ended capacitor to a second end of the first winding; coupling a second end of the second single-ended capacitor to the ground potential; connecting and disconnecting the first single-ended capacitor between the first end of the first winding and the ground potential through the first transistor; and connecting and disconnecting the second single-ended capacitor between a second end of the first winding and the ground potential through the second transistor.

17. The method of claim 16, wherein the pair of differential capacitors comprise a first differential capacitor and a second differential capacitor; wherein the first differential capacitor and the second differential capacitor are a pair of balanced capacitors; wherein a switch is coupled between the first differential capacitor and the second differential capacitor; wherein the method further comprises: connecting and disconnecting the first differential capacitor and the second differential capacitor to and from one another through the switch.

Description

SHORT DESCRIPTION OF DRAWINGS

(1) Embodiments of the invention will be described with respect to the following figures, in which:

(2) FIG. 1 shows a diagram of a resonator circuit according to an embodiment;

(3) FIG. 2 shows a diagram of a radio frequency oscillator according to an embodiment;

(4) FIG. 3 shows an input impedance response and an equivalent circuit of a resonator circuit;

(5) FIG. 4 shows an input impedance response and an equivalent circuit of a resonator circuit according to an embodiment;

(6) FIG. 5 shows a transformer comprising a primary winding and a secondary winding according to an embodiment;

(7) FIG. 6 shows a resonator circuit and an input impedance response according to an embodiment;

(8) FIG. 7 shows a diagram of a radio frequency oscillator according to an embodiment;

(9) FIG. 8 shows a diagram of a single-ended capacitor according to an embodiment;

(10) FIG. 9 shows a diagram of a differential capacitor according to an embodiment;

(11) FIG. 10 shows a diagram of a tail resistor of a radio frequency oscillator according to an embodiment; and

(12) FIG. 11 shows a phase noise power spectral density of a radio frequency oscillator according to an embodiment.

DETAILED DESCRIPTION

(13) FIG. 1 shows a diagram of a resonator circuit 100 according to an embodiment. The resonator circuit 100 comprises a transformer 101 comprising a primary winding 103 and a secondary winding 105, wherein the primary winding 103 is inductively coupled with the secondary winding 105, a primary capacitor 107 being connected to the primary winding 103, the primary capacitor 107 and the primary winding 103 forming a primary circuit, and a secondary capacitor 109 being connected to the secondary winding 105, the secondary capacitor 109 and the secondary winding 105 forming a secondary circuit, wherein the resonator circuit 100 has a common mode resonance frequency at an excitation of the primary circuit in a common mode, wherein the resonator circuit 100 has a differential mode resonance frequency at an excitation of the primary circuit in a differential mode, and wherein the common mode resonance frequency is different from the differential mode resonance frequency. In an embodiment, the common mode resonance frequency is twice the differential mode resonance frequency.

(14) The resonator circuit 100 can be a tank circuit. The resonator circuit 100 can be used as a frequency selective element within a radio frequency oscillator. The resonator circuit 100 can be resonant when excited in the differential mode and in the common mode.

(15) The primary winding 103 and the secondary winding 105 can be arranged to provide a strong inductive coupling when the primary circuit is excited in the differential mode and a weak inductive coupling when the primary circuit is excited in the common mode.

(16) The resonance frequency in differential mode, i.e. the differential mode resonance frequency, can depend on the inductance of the primary winding 103, the capacitance of the primary capacitor 107, the inductance of the secondary winding 105, and the capacitance of the secondary capacitor 109. The resonance frequency in common mode, i.e. the common mode resonance frequency, can depend on the inductance of the primary winding 103 and the capacitance of the primary capacitor 107. The resonance frequency in common mode, i.e. the common mode resonance frequency, may be independent from the inductance of the secondary winding 105, and the capacitance of the secondary capacitor 109.

(17) The diagram illustrates the overall structure of the resonator circuit 100, wherein the primary capacitor 107 can comprise a pair of single-ended capacitors, and wherein the secondary capacitor 109 can comprise a pair of differential capacitors.

(18) FIG. 2 shows a diagram of a radio frequency oscillator 200 according to an embodiment. The radio frequency oscillator 200 comprises a resonator circuit 100, and an excitation circuit 201. The resonator circuit 100 comprises a transformer 101 comprising a primary winding 103 and a secondary winding 105, wherein the primary winding 103 is inductively coupled with the secondary winding 105, a primary capacitor 107 being connected to the primary winding 103, the primary capacitor 107 and the primary winding 103 forming a primary circuit, and a secondary capacitor 109 being connected to the secondary winding 105, the secondary capacitor 109 and the secondary winding 105 forming a secondary circuit, wherein the resonator circuit 100 has a common mode resonance frequency at an excitation of the primary circuit in a common mode, wherein the resonator circuit 100 has a differential mode resonance frequency at an excitation of the primary circuit in a differential mode, and wherein the common mode resonance frequency is different from the differential mode resonance frequency. The excitation circuit 201 is configured to excite the primary circuit of the resonator circuit 100 in the differential mode. The excitation circuit 201 can exemplarily comprise an exciting element, e.g. a feedback amplifier, providing a trans-conductance Gm.

(19) In an embodiment, the excitation circuit 201 comprises at least one transistor, in particular at least one field-effect transistor, for exciting the primary circuit of the resonator circuit 100. In order to realize a cross-coupled oscillator structure at least two transistors may be employed.

(20) In the following, further implementation forms and embodiments of the resonator circuit 100 and the radio frequency oscillator 200 are described.

(21) An up-conversion of flicker noise, e.g. 1/f noise, can degrade a close-in spectrum of a radio frequency oscillator, e.g. a complementary metal-oxide semiconductor (CMOS) radio frequency (RF) oscillator. The resulting 1/f.sup.3 phase noise (PN) can further be an issue within phase-locked loops (PLLs) having a loop bandwidth of e.g. less than 1 MHz, which practically relates to the majority of cellular phones. A major flicker noise up-conversion mechanism in nanoscale CMOS is the Groszkowski effect.

(22) The presence of harmonics in a current of an active device, such as a transistor of an excitation circuit, can cause a frequency drift of a resonance frequency of a resonator circuit, due to perturbing reactive energy in the resonator circuit. Any variation in the ratio of a higher harmonic current to a fundamental current (e.g. due to the flicker noise) can modulate the frequency drift and can show itself as a 1/f.sup.3 phase noise. Embodiments of the invention reduce the flicker noise up-conversion due to the Groszkowski effect in radio frequency oscillators significantly. The resonator circuit 100 can be applied for flicker noise up-conversion reduction within the radio frequency oscillator 200, wherein the radio frequency oscillator 200 can be a class F oscillator.

(23) FIG. 3 shows an input impedance response 301 and an equivalent circuit 303 of a resonator circuit. The diagram illustrates current harmonic paths and frequency drifts for the resonator circuit without resistive traps at higher harmonics.

(24) The presence of harmonics of a current of an active device, such as a transistor of an excitation circuit, can cause a frequency drift of a resonance frequency ω.sub.0 of a resonator circuit as depicted in FIG. 3. A fundamental drain current I.sub.H1 can flow into the resistors having the resistance R.sub.p, which can be the equivalent parallel resistance of the resonator circuit, while its second and third harmonics, I.sub.H2 and I.sub.H3, may mainly take the capacitance path due to its lower impedance. As a consequence, reactive energy stored in the inductors and capacitors, e.g. having inductances L.sub.p and capacitances Cc and Cd, can be perturbed, shifting the resonance frequency ω.sub.0 and/or the oscillation frequency by Aw lower in order to satisfy the resonance condition. This shift may be static but any variation in the ratio of the currents I.sub.H2 (or I.sub.H3) to I.sub.H1 (e.g. due to flicker noise) can modulate Aw and can show itself as a 1/f.sup.3 phase noise.

(25) FIG. 4 shows an input impedance response 401 and an equivalent circuit 403 of a resonator circuit 100 according to an embodiment. The diagram illustrates current harmonic paths and frequency drifts for the resonator circuit 100 with resistive traps at higher harmonics.

(26) Suppose that the input impedance Z.sub.in of the resonator circuit 100 has further peaks at strong harmonics of the fundamental resonance frequency ω.sub.0. These harmonics would then mainly flow into their relative equivalent resistance of Z.sub.in, instead of its capacitive part, as depicted in FIG. 4. Consequently, Groszewski's effect on the flicker noise up-conversion can be reduced significantly. On the other hand, flicker noise of transistors, e.g. core transistors, of an excitation circuit can modulate the second harmonic of the virtual ground of the radio frequency oscillator. This modulation can generate a second harmonic current in parasitic gate-source capacitors C.sub.gs and can get injected into the resonator circuit 100. Consequently, the current I.sub.H2 can be the main contributor to the frequency drift.

(27) In other words, a dominant source of 1/f noise up-conversion in radio frequency oscillators, in particular without tail transistors, is that current harmonics of the resonator circuits flow into the capacitive part of the resonator circuits as shown in FIG. 3. An approach for reducing the 1/f noise up-conversion is illustrated in FIG. 4. For resonance frequencies at higher harmonics, the current can flow into the equivalent resistance of the resonator circuit and 1/f noise up-conversion can be reduced. A resonator circuit 100 is generally shown in FIG. 1.

(28) Embodiments of the invention apply a transformer-based resonator circuit topology that effectively traps the current I.sub.H2 in its resistive part without the cost of extra die area on a semiconductor substrate. The resonator circuit 100 can derive this characteristic from a different behavior of inductors and transformers in differential mode (DM) and common mode (CM) excitations. The transformer based resonator circuit 100 can be incorporated into the radio frequency oscillator 200, e.g. a class-F oscillator, in order to take advantage of its low phase noise in the 20 dB/dec region and in order to improve the phase noise in the 30 dB/dec region.

(29) The resonator circuit 100 can be based on the transformer 101, e.g. being a 1:2 turn transformer. The differential mode resonance frequency and the common mode resonance frequency can be different within the transformer 101, e.g. due to different coupling factors in differential mode and in common mode. An application of a switch is avoided. The resistive trap is realized by the common mode resonance.

(30) The common mode signal that excites the common mode resonance can be the second harmonic component of the current within the resonator circuit 100. The I.sub.H2 component can have a π/2 phase shift with regard to the fundamental current which can make it a common mode signal as illustrated in FIG. 3 and FIG. 4.

(31) If the space of the primary winding and/or the secondary winding is designed accurately and a ratio C.sub.s/C.sub.p is chosen accurately, the common mode resonance frequency can be two times the differential mode resonance frequency. Then, the common mode second harmonic current component can flow into the equivalent resistance of the resonant peak and may not flow through the capacitive part. This approach mitigates disturbances of the reactive energy in the capacitive part and reduces the 1/f noise up-conversion.

(32) FIG. 5 shows a transformer 101 comprising a primary winding 103 and a secondary winding 105 according to an embodiment. The diagram illustrates the currents within the primary winding 103 and the secondary winding 105 when the transformer 101 is excited in differential mode (DM) and in common mode (CM). The transformer 101 can be an F.sub.2,3 transformer.

(33) The primary winding 103 of the transformer 101 and the secondary winding 105 of the transformer 101 are planar and are arranged on the same plane. The secondary winding 105 of the transformer 101 comprises a bridging portion being arranged at a different plane.

(34) The primary winding 103 of the transformer 101 and the secondary winding 105 of the transformer 101 are connected to a supply voltage or an alternating current (AC) ground potential. The connection is realized by a symmetrical center tapping of the primary winding 103 and the secondary winding 105.

(35) The transformer 101, having a 1:2 turn ratio, can be excited by differential mode and common mode input signals at its primary winding 103. In differential mode excitation, the induced currents at the secondary winding 105 can circulate in the same directions leading to a strong coupling factor k.sub.m. On the other hand, in common mode excitation, the induced currents can cancel each other, resulting in a weak coupling factor k.sub.m.

(36) The inductance of the primary winding 103 can be referred to as L.sub.p, the inductance of the secondary winding 105 can be referred to as L.sub.s, the capacitance of the primary capacitor 107 can be referred to as C.sub.p, and the capacitance of the secondary capacitor 109 can be referred to as C.sub.s. According to this definition, the primary winding 103, the secondary winding 105, the primary capacitor 107, and the secondary capacitor 109 are considered as individual concentrated components.

(37) Alternatively, the inductance of the primary winding 103 can be referred to as 2 L.sub.p, the inductance of the secondary winding 105 can be referred to as 2 L.sub.s, the capacitance of the primary capacitor 107 can be referred to as 0.5 C.sub.p, and the capacitance of the secondary capacitor 109 can be referred to as 0.5 C.sub.s. According to this definition, the primary winding 103 and the secondary winding 105 are each formed by a pair of inductors connected in series, wherein the inductance of each inductor is referred to as L.sub.p or L.sub.s, respectively. Furthermore, the primary capacitor 107 and the secondary capacitor 109 are each formed by a pair of capacitors connected in series, wherein the capacitance of each capacitor is referred to as C.sub.p or C.sub.s, respectively.

(38) The differential mode resonance frequency can be determined according to the following equation:

(39) ${\omega }_{0,\mathrm{DM}}=\frac{1}{\sqrt{L_{\mathrm{pd}}{C}_p+L_s{C}_s}}$
wherein ω.sub.0,DM denotes the differential mode resonance frequency, L.sub.pd denotes an inductance associated with the primary winding 103 in differential mode, C.sub.p denotes a capacitance associated with a primary capacitor 107, L.sub.s denotes an inductance associated with the secondary winding 105, and C.sub.s denotes a capacitance associated with a secondary capacitor 109.

(40) The common mode resonance frequency can be determined according to the following equation:

(41) ${\omega }_{\mathrm{CM}}=\frac{1}{\sqrt{L_{\mathrm{pc}}{C}_p}}$
wherein ω.sub.CM denotes the common mode resonance frequency, L.sub.pc denotes an inductance associated with the primary winding 103 in common mode, and C.sub.p denotes a capacitance associated with a primary capacitor 107.

(42) L.sub.pd can relate to half of the inductance of the primary winding 103 in differential mode, e.g. the inductance between a center tap of the primary winding 103 and one of the inputs, yielding a total differential primary capacitance of 2 L.sub.p. This is due to the consideration that the inductance L.sub.T may not be seen in differential excitation but may affect the inductance in common mode excitation. The total inductance in common mode excitation can be equal to 2 L.sub.pd+2 L.sub.T, or L.sub.pc=L.sub.pd+L.sub.T as used in the equations.

(43) In an embodiment, the inductance associated with the primary winding 103 in differential mode and the inductance associated with the primary winding 103 in common mode are considered to be equal.

(44) FIG. 6 shows a resonator circuit 100 and an input impedance response 609 according to an embodiment. The resonator circuit 100 comprises a transformer 101 comprising a primary winding 103 and a secondary winding 105, wherein the primary winding 103 is inductively coupled with the secondary winding 105, a primary capacitor 107 being connected to the primary winding 103, the primary capacitor 107 and the primary winding 103 forming a primary circuit, and a secondary capacitor 109 being connected to the secondary winding 105, the secondary capacitor 109 and the secondary winding 105 forming a secondary circuit, wherein the resonator circuit 100 has a common mode resonance frequency at an excitation of the primary circuit in a common mode, wherein the resonator circuit 100 has a differential mode resonance frequency at an excitation of the primary circuit in a differential mode, and wherein the common mode resonance frequency is different from the differential mode resonance frequency. FIG. 6 shows a possible realization of the resonator circuit 100.

(45) The primary capacitor 107 of the primary circuit comprises a pair of single-ended capacitors 601, 603. The secondary capacitor 109 of the secondary circuit comprises a pair of differential capacitors 605, 607. The primary capacitor 107 and the secondary capacitor 109 are variable capacitors, in particular digitally tunable capacitors. In particular, the pair of single-ended capacitors 601, 603 and the pair of differential capacitors 605, 607 are variable capacitors, in particular digitally tunable capacitors. The differential mode resonance frequency and/or the common mode resonance frequency are tunable between a minimum frequency f.sub.min and a maximum frequency f.sub.max, respectively, as illustrated by the input impedance response 609. The input impedance of the resonator circuit 100 is denoted as Z.sub.in.

(46) The resonator circuit 100 can employ the transformer 101, the pair of single-ended capacitors 601, 603 within the primary circuit and the pair of differential capacitors 605, 607 within the secondary circuit. The resonator circuit 100 can be an F.sub.2,3 resonator circuit. The transformer 101 can be an F.sub.2,3 transformer. The resonator circuit 100 can have two differential mode resonance frequencies and one common mode resonance frequency.

(47) For class-F.sub.3 operation, ω.sub.1,DM=3ω.sub.0,DM, and for resistive traps at the second and third harmonics, ω.sub.CM=2ω.sub.0,DM and ω.sub.1,DM=3ω.sub.0,DM. This can result in L.sub.sC.sub.s=3L.sub.pC.sub.p and k.sub.m=0.72, wherein k.sub.m denotes the coupling factor between the primary winding 103 and the secondary winding 105.

(48) When implementing the resonator circuit 100, the inductance associated with the primary winding 103 in common mode L.sub.pc can be greater than the inductance associated with the primary winding 103 in differential mode L.sub.pd, i.e. L.sub.pc>L.sub.pd, due to a metal track inductance L.sub.T connecting e.g. a center tap of the primary winding 103 to a constant supply voltage. Thus, a lower coupling factor k.sub.m may be used in order to satisfy both F.sub.2 and F.sub.3 operation conditions of the resonator circuit 100. A careful design of the single-ended capacitors 601, 603 within the primary circuit and/or the differential capacitors 605, 607 within the secondary circuit, which can be variable capacitors, can maintain ω.sub.CM/ω.sub.0,DM≈2 and ω.sub.1,DM/ω.sub.0,DM≈3 over the full tuning range (TR).

(49) In an embodiment, the inductance associated with the primary winding 103 in common mode L.sub.pc is determined according to the following equation:
L.sub.pc=L.sub.pd+L.sub.T
wherein L.sub.pc denotes the inductance associated with the primary winding 103 in common mode, L.sub.pd denotes the inductance associated with the primary winding 103 in differential mode, and L.sub.T denotes the metal track inductance.

(50) FIG. 7 shows a diagram of a radio frequency oscillator 200 according to an embodiment. The radio frequency oscillator 200 comprises a resonator circuit 100, and an excitation circuit 201. The resonator circuit 100 forms an implementation of the resonator circuit 100 as described in conjunction with FIG. 6. The excitation circuit 201 comprises a transistor 701, a transistor 703, a tail resistor 705, and a tail capacitor 707. The radio frequency oscillator 200 is a class F oscillator.

(51) Class F.sub.3 oscillators can have a pseudo square-wave oscillation waveform by designing ω.sub.1,DM=3.sub.ω0,DM, and avoiding filtering the current I.sub.H3 in a resonator circuit. The specific impulse sensitivity function (ISF) of the pseudo square-wave oscillation waveform can lead to an improved phase noise performance. In this oscillator, the current I.sub.H2 can be as high as the current I.sub.H3. In a class F.sub.2,3 oscillator, a class F.sub.3 resonator circuit is replaced by a class F.sub.2,3 resonator circuit. The pseudo square-wave oscillation waveform of class F oscillators can be preserved, wherein a 1/f.sup.3 phase noise corner frequency can be reduced e.g. from 300 kHz to 700 kHz to less than 30 kHz. Embodiments of the invention use an F.sub.2,3 resonator circuit and the different characteristics of a 1:2 turn transformer in differential mode and common mode excitations in order to provide a resistive trap at the second harmonic 2ω.sub.0, resulting in a reduction of flicker noise up-conversion in radio frequency oscillators.

(52) FIG. 8 shows a diagram of a single-ended capacitor 601, 603 according to an embodiment. The single-ended capacitor 601, 603 comprises a capacitor 801, a capacitor 803, a transistor 805, a transistor 807, a resistor 809, a resistor 811, an inverter 813, and an inverter 815. The single-ended capacitor 601, 603 is arranged within the primary circuit.

(53) By applying a digital switching signal b.sub.i, the transistor 805 and the transistor 807 can be switched between a conducting state and a non-conducting state. Consequently, the capacitance of the single-ended capacitor 601, 603 can be digitally tuned. A plurality of single-ended capacitors 601, 603 can be connected in parallel.

(54) FIG. 9 shows a diagram of a differential capacitor 605, 607 according to an embodiment. The differential capacitor 605, 607 comprises a capacitor 901, a capacitor 903, a transistor 905, a resistor 907, a resistor 909, an inverter 911, and an inverter 913. The differential capacitor 605, 607 is arranged within the secondary circuit.

(55) By applying a digital switching signal b.sub.i, the transistor 905 can be switched between a conducting state and a non-conducting state. Consequently, the capacitance of the differential capacitor 605, 607 can be digitally tuned. A plurality of differential capacitors 605, 607 can be connected in parallel.

(56) FIG. 10 shows a diagram of a tail resistor 705 of a radio frequency oscillator 200 according to an embodiment. The tail resistor 705 comprises a transistor 1001, and a resistor 1003. The tail resistor 705 can be used for current control within the radio frequency oscillator 200.

(57) By applying a digital switching signal b.sub.i, the transistor 1001 can be switched between a conducting state and a non-conducting state. Consequently, the current within the radio frequency oscillator 200 can be controlled. A plurality of tail resistors 705 can be connected in parallel and/or in series.

(58) FIG. 11 shows a phase noise power spectral density 1101 of a radio frequency oscillator 200 according to an embodiment. The diagram depicts the phase noise power spectral density in dBc/Hz over a carrier frequency offset in Hz. The radio frequency oscillator 200 is a class F.sub.2,3 oscillator.

(59) The diagram relates to a minimum frequency of 5.4 GHz and a maximum frequency of 7 GHz. A 1/f.sup.3 phase noise corner is further depicted in the diagram.

(60) It will be appreciated that statements made herein characterizing the invention refer to an embodiment of the invention and not necessarily all embodiments.