A circuit comprising a differential transmission line and eight switches provides non-reciprocal signal flow. In some embodiments, the circuit can be driven by four local oscillator signals using a boosting circuit. The circuit can be used to form a gyrator. The circuit can be used to form a circulator. The circuit can be used to form three-port circulator than can provide direction signal flow between a transmitter and an antenna and from the antenna to a receiver. The three-port circulator can be used to implement a full duplex transceiver that uses a single antenna for transmitting and receiving.

BACKGROUND

Full-duplex communications, in which a transmitter and a receiver of a transceiver operate simultaneously on the same frequency band, is drawing significant interest for emerging 5G communication networks due to its potential to double network capacity compared to half-duplex communications. Additionally, there are several efforts underway to include simultaneous transmit and receive functionality in the next generation phased array radar systems, especially in commercial automotive radars which can be an enabler technology for future connected or driverless cars. However, one of the biggest challenges from an implementation perspective is the antenna interface.

One way in which an antenna interface for a full-duplex transceiver can be implemented is using a non-reciprocal circulator. Reciprocity in electronics is a fundamental property of linear systems and materials described by symmetric and time-independent permittivity and permeability tensors. Non-reciprocity causes signals to travel in only one direction. For example, non-reciprocity in a circulator causes signals to travel in only one direction through the circulator. This directional signal flow enables full-duplex wireless communications because signals from the transmitter are only directed toward the antenna (and not the receiver) and received signals at the antenna are only directed toward the receiver (and not the transmitter). Moreover, the receiver is isolated from signals from the transmitter, preventing desensitization and possible breakdown of the receiver due to the high-power transmitted signal.

Conventionally, non-reciprocal circulators have been implemented using ferrite materials, which are materials that lose their reciprocity under the application of an external magnetic field. However, ferrite materials cannot be integrated into CMOS IC technology. Furthermore, the need for an external magnet renders ferrite-based circulators bulky and expensive.

Accordingly, new mechanisms for implementing non-reciprocity in circuits is desirable.

SUMMARY

In accordance with some embodiments, magnetic-free non-reciprocal circuits based on sub-harmonic spatio-temporal conductance modulation are provided. In some embodiments, circuits are provided, the circuits comprising: a first differential transmission line having: a first end having a first connection and a second connection; and a second end having a third connection and a fourth connection; a first switch having a first side, a second side, and a control, wherein the first side of the first switch is connected to the first connection; a second switch having a first side, a second side, and a control, wherein the first side of the second switch is connected to the first connection; a third switch having a first side, a second side, and a control, wherein the first side of the third switch is connected to the second connection and the second side of the third switch is connected to the second side of the first switch and a first node; a fourth switch having a first side, a second side, and a control, wherein the first side of the fourth switch is connected to the second connection and the second side of the fourth switch is connected to the second side of the second switch and a second node; a fifth switch having a first side, a second side, and a control, wherein the first side of the fifth switch is connected to the third connection; a sixth switch having a first side, a second side, and a control, wherein the first side of the sixth switch is connected to the third connection; a seventh switch having a first side, a second side, and a control, wherein the first side of the seventh switch is connected to the fourth connection and the second side of the seventh switch is connected to the second side of the fifth switch and a third node; an eighth switch having a first side, a second side, and a control, wherein the first side of the eighth switch is connected to the fourth connection and the second side of the eighth switch is connected to the second side of the sixth switch and a fourth node; and at least one boosting circuit that, in response to a modulation signal drives the control of at least one of the control of the first switch, the control of the second switch, the control of the third switch, the control of the fourth switch, the control of the fifth switch, the control of the sixth switch, the control of the seventh switch, and the control of the eighth switch with a drive signal.

DETAILED DESCRIPTION

FIGS. 1A, 1B, 1C, and 1Dshow an example of how a non-reciprocal phase shift can be implemented in some embodiments.

Turning toFIG. 1A, it can be seen that a signal cos(ωint) can be injected at nodes A. This is represented in graph101ofFIG. 1B. As shown inFIG. 1A, the switch groups can then be switched by the following signals: cos(ωmt); cos(ωmt+Φ); sin(ωmt); and sin(ωmt+Φ), where Φ is 90°. Φ1and Φ2shown inFIGS. 1A and 1Brelate to Φ according to the following equation: 2Φ=180=Φ1−Φ2(or equivalently, 2*Td*ωm/π=1 where Td is the delay of the transmission lines). As a result of the switching at the switch groups closest to nodes A, the input signal is commutated and two mixing products appear after the commutation on each transmission line at ωin−ωmand ωin+ωm. These signals then flow through the top and bottom transmission lines (which provide −Φ1and −Φ2phase shifts at ωin−ωmand ωin+ωm, respectively). The mixing tones flowing through the top transmission line appear at node B1Fwith total phase shifts of −Φ1and −Φ2at ωin−ωmand ωin+ωm, respectively. The mixing tones flowing through the bottom line appear at node B2Fwith total phase shifts of −Φ1+90° and −Φ2−90°) at ωin−ωmand ωin+ωm, respectively. This is shown in graph102ofFIG. 1B. The phase shifted signals are then commutated again at ωm, by the switch groups closest to nodes C, but with a phase shift of Φ. For each of the four signals in graph102, two mixing products appear after the commutation at nodes C (for a total of eight signals). As shown in graph103ofFIG. 1B, the mixing products appear at ωin−2ωm, ωin, and ωin+2ωmwith phase shifts as shown in the following table:

As can be seen, the signals at ωin−2ωmand ωin+2ωm(in rows 1 and 5 and rows 4 and 8, respectively) are 180° out of phase and thus cancel out. Also, the signals at ωin(in rows 2, 3, 6, and 7) all have the same phase, and thus add up into a single signal with a phase shift of Φ−Φ1, or 90°−Φ1. This is shown in graph104ofFIG. 1B.

Turning toFIG. 1C, it can be seen that a signal cos(ωint) can be injected at nodes C. This is represented in graph111ofFIG. 1D. As shown inFIG. 1C, the switch groups are switched by the following signals: cos(ωmt); cos(ωmt+Φ); sin(ωmt); and sin(ωmt+Φ), where Φ is 90°. Φ1and Φ2shown inFIGS. 1C and 1Drelate to Φ according to the following equation: 2Φ=180=Φ1−Φ2(or equivalently, 2*Td*ωm/π=1 where Td is the delay of the transmission lines). As a result of the switching at the switch groups closest to nodes C, the input signal is commutated and two mixing products appear after the commutation on each transmission line at ωin−ωm(with phase shifts of −Φ) and Φin+ωm(with phase shifts of Φ). These signals then flow through the top and bottom transmission lines (which provide −Φ1and −Φ2phase shifts at ωin−ωmand ωin+ωm, respectively). The mixing tones flowing through the top transmission line appear at node B1Rwith total phase shifts of −Φ−Φ1and Φ−Φ2at ωin−ωmand ωin+ωm, respectively. The mixing tones flowing through the bottom line appear at node B2Rwith total phase shifts of 90°−Φ−Φ1and −90°+Φ1−Φ2at ωin−ωmand ωin+ωm, respectively. This is shown in graph112ofFIG. 1D. The phase shifted signals are then commutated again at ωm, by the switch groups closest to nodes A. For each of the four signals in graph112, two mixing products appear after the commutation at nodes A (for a total of eight signals). As shown in graph113ofFIG. 1D, the mixing products appear at ωin−2ωm, ωin, and ωin+2ωmwith phase shifts as shown in the following table:

As can be seen, the signals at ωin−2ωmand ωin+2ωm(in rows 1 and 5 and rows 4 and 8, respectively) are 180° out of phase and thus cancel out. Also, the signals at ωin(in rows 2, 3, 6, and 7) all have the same phase, and thus add up into a single signal with a phase shift of −Φ−Φ1, or −90°−Φ1. This is shown in graph114ofFIG. 1D.

As can be seen inFIGS. 1C and 1D, the signals at ωinincur different phase shifts in the forward and reverse direction (Φ−Φ1and −Φ−Φ1, respectively), demonstrating the phase non-reciprocity.

The scattering parameter matrix of the configuration shown inFIGS. 1A, 1B, 1C, and 1Dcan be represented by [S] as follows:

[S]=[0ej⁡(-ϕ-ϕ1)ej⁡(ϕ-ϕ1)0]
where: j is the square root of −1. The −ϕ in the term on the top right corner and +ϕ in the term on the bottom left corner show that the phase is non-reciprocal.

FIGS. 2A, 2B, 2C, and 2Dshow an example of how non-reciprocal amplitude (an isolator) can be implemented in some embodiments.

Turning toFIG. 2A, it can be seen that a signal cos(ωint) can be injected at nodes A. This is represented in graph201ofFIG. 2B. As shown inFIG. 2A, the switch groups can then be switched by the following signals: cos(ωmt); cos(ωmt+Φ); sin(ωmt); and sin(ωmt+Φ), where Φ is 45°. Φ1and Φ2shown inFIGS. 2A and 2Brelate to Φ according to the following equation: 2Φ=90°=Φ1−Φ2(or equivalently, 4*Td*ωm/π=1 where Tdis the delay of the transmission lines). As a result of the switching at the switch groups closest to nodes A, the input signal is commutated and two mixing products appear after the commutation on each transmission line at ωin−ωmand ωin+ωm. These signals then flow through the top and bottom transmission lines (which provide −Φ1and −Φ2phase shifts at ωin−ωmand ωin+ωm, respectively). The mixing tones flowing through the top transmission line appear at node B1Fwith total phase shifts of −Φ1and −Φ2at ωin−ωmand ωin+ωm, respectively. The mixing tones flowing through the bottom line appear at node B2Fwith total phase shifts of −Φ1+90° and −Φ2−90°) at ωin−ωmand ωin+ωm, respectively. This is shown in graph202ofFIG. 2B. The phase shifted signals are then commutated again at ωm, by the switch groups closest to nodes C, but with a phase shift of Φ. For each of the four signals in graph202, two mixing products appear after the commutation at nodes C (for a total of eight signals). As shown in graph203ofFIG. 2B, the mixing products appear at ωin−2ωm, ωin, and ωin+2ωmwith phase shifts as shown in the following table:

As can be seen, the signals at ωin−2ωmand ωin+2ωm(in rows 1 and 5 and rows 4 and 8, respectively) are 180° out of phase and thus cancel out. Also, the signals at ωin(in rows 2, 3, 6, and 7) all have the same phase, and thus add up into a single signal with a phase shift of Φ−Φ1, or 45°−Φ1. This is shown in graph204ofFIG. 2B.

Turning toFIG. 2C, it can be seen that a signal cos(ωint) can be injected at nodes C. This is represented in graph211ofFIG. 2D. As shown inFIG. 2C, the switch groups can then be switched by the following signals: cos(ωmt); cos(ωmt+Φ); sin(ωmt); and sin(ωmt+Φ), where Φ is 45°. Φ1and Φ2shown inFIGS. 2C and 2Drelate to Φ according to the following equation: 2Φ=90=Φ1−Φ2(or equivalently, 4*Td*ωm/π=1 where Td is the delay of the transmission lines). As a result of the switching at the switch groups closest to nodes C, the input signal is commutated and two mixing products appear after the commutation on each transmission line at ωin−ωm(with phase shifts of −Φ) and Φin+ωm(with phase shifts of Φ). These signals then flow through the top and bottom transmission lines (which provides −Φ1and −Φ2phase shifts at ωin−ωmand ωin+ωm, respectively). The mixing tones flowing through the top transmission line appear at node B1R with total phase shifts of −Φ−Φ1and Φ−Φ2at ωin−ωmand ωin+ωm, respectively. The mixing tones flowing through the bottom line appear at node B2R with total phase shifts of 90°−Φ−Φ1and −90°+Φ−Φ2at ωin−ωmand ωin+ωm, respectively. This is shown in graph212ofFIG. 2D. The phase shifted signals are then commutated again at ωm, by the switch groups closest to nodes A. For each of the four signals in graph212, two mixing products appear after the commutation at nodes A (for a total of eight signals). As shown in graph213ofFIG. 2D, the mixing products appear at ωin−2ωm, ωin, and ωin+2ωmwith phase shifts as shown in the following table:

As can be seen, the signals at ωin−2ωm, ωin, and ωin+2ωm(in rows 1 and 5, rows 2, 3, 6, and 7, and rows 4 and 8, respectively) are 180° out of phase and thus cancel out. This is shown in graph214ofFIG. 2D.

As can be seen inFIGS. 2C and 2D, the signal at ωincan only pass in the forward direction while it is completely attenuated in the reverse direction, showing amplitude non-reciprocity.

FIGS. 2A, 2B, 2C, and 2Ddescribe an isolator configuration, where signals can travel in one direction but not the reverse direction. An isolator is like one arm of a circulator. It is useful because it can be placed between a power amplifier and its antenna, and it will protect the power amplifier from back reflections at the antenna.

Another use of the structures ofFIGS. 1A, 1B, 2A, and 2Bis a 2D lattice of such structures which can have a programmable signal propagation based on the phase shifts of the different switches.

InFIGS. 1A, 1B, 2A, and 2B, mixing products at ωin−ωmand ωin+ωmhave been shown for simplicity, but, in reality, square-wave commutation can produce mixing products at offsets equal to all odd multiples of ωm.

Turning toFIG. 3, an example300of a circulator architecture in accordance with some embodiments is shown. As illustrated, circulator300includes an antenna port301, a transmitter port302, a receiver port304, a non-reciprocal phase component306, and transmission lines308,310, and312. Within non-reciprocal phase component306, there are passive mixers314,316,318, and320, and transmission lines322and324.

As shown inFIG. 3, values of signals and components in non-reciprocal phase component306may depend on an input frequency (ωin) and a modulation frequency (ωm). ωinrepresents the frequency of operation of the circulator. ωmrepresents the frequency at which the mixers are modulated. Any suitable frequencies can be used for ωinand ωm, in some embodiments. For example, in some embodiments, RF/millimeter-wave/Terahertz frequencies can be used. In some embodiments, ωinand ωmmay be required to be sized relative to each other. For example, in some embodiments, the mixing signals at ωin+ωmand ωin−ωmshould be 180° out of phase or equivalently the following equation may be required to be met: 2ωmTd=180°, where Tdis the group delay. More particularly, for example, in some embodiments, ωincan be 28 GHz and ωmcan be 9.33 GHz.

Each of the transmission lines inFIG. 3is illustrated as having a “length” that is based on a given frequency. For example, transmission lines308,310, and312are illustrated as having a length equal to λ/4, where λ is the wavelength for a frequency of ωin. As another example, transmission lines322and324are illustrated as providing 180° phase difference between the signals at ωin+ωmand ωin−ωmor equivalently a group delay of Td=¼(ωm/2π).

Transmission lines308,310,312,322, and324can be implemented in any suitable manner. For example, in some embodiments, one or more of the transmission lines can be implemented as C-L-C pi-type lumped sections. In some other embodiments, they may be implemented as truly distributed transmission lines.

The passive mixers can be driven by signals as shown inFIG. 3, in some embodiments. For example, in some embodiments, mixer314can be driven by a signal cos(ωmt), mixer316can be driven by a signal cos(ωmt+Φ), mixer318can be driven by a signal sin(ωmt), and mixer320can be driven by a signal sin(ωmt+Φ), where Φ is 90° for Td=¼(ωm/2π).

In some embodiments, mixers314,316,318, and320shown inFIG. 3can be implemented with switch groups414,416,418, and420, respectively, as illustrated inFIG. 4A. As shown inFIG. 4B, the switch groups inFIG. 4Acan each include four switches402,404,406, and408, in some embodiments.

The switches in the switch groups can be implemented in any suitable manner. For example, in some embodiments, the switches can be implemented using NMOS transistors, PMOS transistors, both NMOS and PMOS transistors, or any other suitable transistor or any other switch technology.

Switch groups414,416,418, and420can be controlled by local oscillator signals LO1, LO2, LO1Q, and LO2Q, respectively, as shown inFIG. 4A, in some embodiments. A timing diagram showing an example of these signals with respect to each other is shown inFIG. 4C. In this diagram, fLOis equal to ωm/2π. When a local oscillator (e.g., LO1, LO2, LO1Q, or LO2Q) is HIGH, switches402and408in the corresponding switch group are CLOSED and switches404and406in the corresponding switch group are OPEN. When a local oscillator (e.g., LO1, LO2, LO1Q, or LO2Q) is LOW, switches404and406in the corresponding switch group are OPEN and switches404and406in the corresponding switch group are CLOSED.

Turning toFIG. 5, an example of a schematic of a circulator that can be implemented in accordance with some embodiments is shown. This circulator is generally in the same architecture as shown inFIG. 3, except that transmission line308is split in half and part is placed adjacent to the receiver nodes.

The differential nature of the circulator can reduce the LO feedthrough and improve power handling. The fully-balanced I/Q quads can be designed using 2×16 μm/40 nm floating-body transistors. The placement of the gyrator in a symmetric fashion between the TX and RX ports can be used to enable switch parasitics to be absorbed into the lumped capacitance of the λ/8 sections on either side. Artificial (quasi-distributed) transmission lines with inductor Q of 20 can be used in the gyrator, using four stages of lumped it-type C-L-C sections with a Bragg frequency of 83.9 GHz. The λ/4 transmission lines between the TX and ANT and ANT and RX ports can be implemented using differential conductor-backed coplanar waveguides. As shown, baluns can be included at the TX, ANT and RX ports to enable single-ended measurements, and separate test structures can be included to de-embed the response of the baluns.

Turning toFIG. 6, an example of the architecture ofFIG. 3using 1-stage lattice filters instead of transmission lines322and324(FIG. 3) is shown. Any suitable filters can be used. For example, in some embodiments, film bulk acoustic resonator (FBAR) filters, surface acoustic wave (SAW) filters, bulk acoustic wave (BAW) filters, and/or any other suitable filters can be used. By implementing large delays using SAW or BAW filters, the clock frequency can be even further reduced. This can be exploited to design even-higher-linearity circulators through the use of high-voltage technologies and high-linearity switch design techniques.

The circuits described herein can be implemented in any suitable technology in some embodiments. For example, in some embodiments, these circuits can be implemented in any semiconductor technology such as silicon, Gallium Nitride (GaN), Indium phosphide (InP), Gallium arsenide (GaAs), etc. More particularly, for example, in some embodiments, the circuits can be implemented in IBM 45 nm SOI CMOS process.

InFIG. 1, the phase shift provided by the non-reciprocal phase component, Φ−Φ1, can be tuned by changing the clock phase, Φ. The frequency at which TX-to-RX isolation is achieved depends on Φ−Φ1, so by tuning Φ, the isolation frequency can be tuned.

Turning toFIG. 7, another example of some embodiments is shown. As illustrated, a spatio-temporal conductivity modulation concept in accordance with some embodiments can include two sets of switches implemented in a fully-balanced fashion on either end of a differential transmission line delay. The switches can be modulated between short and open circuit states through periodic square pulses with a 50% duty cycle. As shown, the transmission line provides a delay equal to one quarter of the modulation period (Tm/4), and the modulation of the right switches is delayed with respect to those on the left by the same amount (Tm/4). Adding this delay between the two sets of switches allows incident signals from different directions to follow different paths, breaking reciprocity.

FIGS. 8A, 8B, and 8Cdepict an example of signal propagation in the forward direction (from left, or port 1, to right, or port 2) in accordance with some embodiments. As shown inFIG. 8A, during the first half-period of the modulation clock, when LO1+ is high, the incident signal goes into the transmission line, gets delayed by the transmission line delay of Tm/4, and reaches to the second set of switches. At this instant, LO2+ is high, so that the signal directly passes to the output. A similar explanation holds also for the second half-period of the modulation clock (shown inFIG. 8B): the signal goes into the transmission line with a sign flip, gets delayed by Tm/4, and the sign flip is recovered by the second set of switches. In other words, signals traveling in the forward direction experience no polarity inversion in the first half cycle, and two polarity inversions negate each other occur in the second half cycle. Thus, effectively, in the forward direction, signals pass through the structure without any loss and experience a delay of one quarter of the modulation period. This can be described by the time domain equation:

v2-⁡(t)=v1+⁡(t-Tm4)
where v1+and v2−are the incident and transmitted signals at ports 1 and 2, respectively.

Alternatively, this structure can be modeled by multiplication, delay and multiplication as depicted inFIG. 8C. Here, the fully-balanced switching operation is modeled as multiplication by a 50% duty cycle clock, m(t), flipping between +1 and −1. Thus, the output signal can be written as:

v2-⁡(t)=v1+⁡(t-Tm4)⁢m⁡(t-Tm4)⁢m⁡(t-Tm4)=v1+⁡(t-Tm4)(1)
which takes advantage of the fact that

The signal propagation in the backward direction (from right to left) is shown inFIGS. 9A, 9B, and 9C. As shown inFIG. 9A, during the first half-period of the modulation clock, when LO2+ is high, the signal goes into the transmission line and gets delayed by Tm/4, and the second set of switches flips the signal sign. Similarly, during the second half-period of the modulation clock (LO2− is high), the signal goes into the transmission line with a sign flip, gets delayed by Tm/4 and reaches the output as LO1+ is high. In brief, signals traveling from right to left experience a transmission line delay of Tm/4 and a polarity inversion in both half cycles. This can be described by:

v1-⁡(t)=-v2+⁡(t-Tm4)
where v2+and v1−are the incident and transmitted signals at ports 1 and 2, respectively.

An analysis based on the signal flow diagram inFIG. 9Cgives

From (1) and (2), the resultant S-parameters can be written as

S2⁢1⁡(ωi⁢n)=e-j⁢π2⁢(ωi⁢nωm)(3)S1⁢2⁡(ωi⁢n)=-e-j⁢π2⁢(ωi⁢nωm)(4)
where ωinand ωmare the signal and modulation frequencies, respectively. It should be noted S11=S22=0 since there is a pair of switches which connects the transmission line to the input and output at any instant in both half cycles. As can be seen from (3) and (4), this generalized spatio-temporal conductivity modulation technique is ideally lossless and breaks phase reciprocity over a theoretically infinite bandwidth. More importantly, it operates as an ideal passive lossless gyrator—a basic non-reciprocal component that provides a non-reciprocal phase difference of π and can be used as a building block to construct arbitrarily complex non-reciprocal networks—over theoretically infinite bandwidth. In practice, the insertion loss would be limited by ohmic losses in the switches and transmission line, and bandwidth by dispersion effects in the transmission line, particularly if it is implemented in a quasi-distributed fashion to absorb the capacitive parasitics of the switches.

FIG. 10shows an example of an illustration of forward and reverse insertion phases (∠S21 and ∠S12, respectively) across frequency normalized to the modulation clock frequency. As can be seen, the spatio-temporal conductivity modulation provides a phase shift of +/−90 degrees at the odd multiples of the modulation frequency, namely ωin=(2n−1)ωm, where n is a positive integer. Using higher odd multiples reduces the clock frequency, which eases clock generation and distribution, at the expense of a longer transmission line which introduces more loss and larger form factor. In some embodiments, an operating to modulation frequency ratio of 3(ωm=ωin/3=8.33 GHz) can be used to optimize this trade-off.

In some embodiments, duty cycle impairment in the modulation clock can have an adverse effect on operation in the reverse direction. For example, let us assume a deviation from ideal 50% duty cycle by ΔTm. The forward direction remains unaffected, since m(t−Tm/4)m(t−Tm/4) continues to be +1, but in the reverse direction, m(t−Tm/2)m(t) will give a pulse train with a pulse width of ΔT and period of Tm/2 as depicted inFIG. 11. Thus, deviation from 50% duty cycle would result in loss in the reverse direction, as some portion of the power would be transferred to mixing frequencies due to the 2ωmcontent in m(t−Tm/2)m(t). S12at the operating frequency becomes

As shown inFIG. 12A, a non-reciprocal phase shift element (gyrator) can be embedded within a 3λ/4 transmission line ring to realize a non-reciprocal circulator in accordance with some embodiments. In the clockwise direction, the −270 degree phase shift of the transmission line adds to the −90 degree phase shift through the gyrator, enabling wave propagation (−270+−90=−360). In the counter-clockwise direction, the −270 degree phase shift of the transmission line adds to the +90 degree phase shift of the gyrator, suppressing wave propagation (−270++90=−180).

A three-port circulator can be realized in some embodiments by introducing three ports λ/4 apart from each other as shown inFIG. 12B. The gyrator can placed symmetrically between the TX and RX ports in some embodiments. The S-parameters of the circulator at ωin=3ωmcan be derived to be:

(00-1-j000-j0)
where TX is port 1, ANT is port 2, and RX is port 3.

FIG. 13shows an example of a block diagram and circuit diagrams of an 8.33 GHz LO path in accordance with some embodiments. As illustrated, the four quadrature clock signals driving the switches can be generated from two input differential sinusoidal signals at 8.33 GHz. A two-stage poly-phase filter (phase imbalance <2 degrees for up to 15% variation in R and C values) can be used to generate the 8.33 GHz quadrature signals with 0/90/180/270 degree phase relationship. After the poly-phase filter, a three stage self-biased CMOS buffer chain with inductive peaking in the final stage can be used to generate the square wave clock signals for the switches. Independently controlled NMOS varactors (implemented using 4×40 μm/40 nm floating-body devices) can be placed at the differential LO inputs to compensate for I/Q imbalance of the poly-phase filter. This provides an I/Q calibration range of +/−10 degrees that can be used optimize the circulator performance.

Turning toFIG. 14A, a switch that can be used in the passive mixers described above (e.g., any one or more of switches402,404,406, and408ofFIG. 4B) is illustrated. As shown, the switch may have a clock (clk) at its gate and an input signal (Vin) at its source. An impedance ZLmay be present at the switch's drain.

A passive mixer compresses when the RF swing on the source/drain of the transistor becomes comparable to the modulation signal at the gate. For a large enough RF swing, the mixer is modulated by the RF signal rather than the modulation signal resulting in false switching and hence compression.

As shown inFIG. 14B, when Vin(represented by the sine wave shown) gets large, for given high and low voltage levels (VHIGHand VLOW, respectively) of the clock, the difference between the high voltage level and the input signal divided by two can be less than the threshold voltage of the switch, and the difference between the input signal divided by two and the low voltage level can be greater than the threshold voltage of the switch. This can cause improper behavior of the switch.

In accordance with some embodiments mechanisms for clock boosting are provided that can address this problem. These mechanisms produce a larger modulation signal thereby enabling mixers to handle higher RF power.

Turning toFIG. 15, an example of a mechanism for clock boosting in accordance with some embodiments is illustrated. As shown, this mechanism includes an inverter at the left, eight switches numbered 1-8, capacitors C1and C2, and a switch at the right (which is part of a passive mixer). In some embodiments, the inverter need not be added to an existing design and the signal LO provided at the output of the inverter can be provided by any suitable component of a circuit that has been designed to drive a passive mixer's switch.

During operation, when the output (LO) of the driving inverter (the driver) is high (+VDD), the output of the driver is level shifted using a pre-charged capacitor (C1, which is charged to +VDD) to create a high output level of +2VDDas shown in the timing diagram on the right ofFIG. 15. When the output of the driving inverter is low (0 Volts), the output of the driver is level shifted using a pre-charged capacitor (C2, which is charged to −VDD) to create a low output level of −VDD. Hence, the output swing of the driving inverter is boosted to create a 3× higher modulation swing. That is, as shown in the timing diagram on the right ofFIG. 15, the signal driving the gate of the switch transitions between −Vdd and +2Vdd instead of between 0 and Vdd.

The function performed by the circuit ofFIG. 15can be represented by the following equation:

In the timing diagram, the voltages VC1and VC2across capacitors C1and C2are shown as being constant even though slight variations in these voltages may occur due to parasitic in the path between the driver and the gate. Although + and − symbols are shown in the figure to provide a reference for voltage measurements, these symbols do not denote that the capacitors are or need to be polarized.

FIGS. 16 and 17further illustrate the operation of the circuit shown inFIG. 15in accordance with some embodiments. As shown inFIG. 16, when the output of the driver is high (e.g., +Vdd), switch1,2,7, and8are closed, and switches3,4,5, and6are open. This causes the voltage across capacitor C1(+Vdd) to be added to the signal (+Vdd) at the output of the driver to produce +2Vdd at the gate of the switch (represented inFIG. 16by Cload). At the same time, capacitor C2is charged to −Vdd. As shown inFIG. 17, when the output of the driver is low (e.g., 0V), switch1,2,7, and8are open, and switches3,4,5, and6are closed. This causes the voltage across capacitor C2(−Vdd) to be added to the signal (0V) at the output of the driver to produce −Vdd at the gate of the switch (represented inFIG. 17by Cload). At the same time, capacitor C1is charged to +Vdd.

For purposes of illustration, it can be assumed that the switches ofFIGS. 15, 16, and 17are implemented using NMOS transistors, such that when a high signal is applied at the gate of the switch, the switch is closed and such that when a low signal is applied at the gate of the switch, the switch is opened.

Turning toFIG. 18, an example of an implementation of the circuit ofFIG. 15in accordance with some embodiments is shown. As illustrated, switches1,2,7, and8can be implemented using PMOS transistors and switches3,4,5, and6can be implemented using NMOS transistors. As also illustrated, the gates of transistors1,3,5, and7can be driven by signal LO, the gates of transistors2and6can be driven by signal LOCPN, and the gates of transistors4and8can be driven by signal LOCPP. LOCPNand LOCPP(andLOCPNandLOCPP) can be generated by a level shift circuit shown in the right ofFIG. 18. Mathematically, LOCPN, LOCPP,LOCPN, andLOCPPcan be represented as:
LO_CPN=−Vdd+LO
LOCPN=−Vdd+LO;
LO_CPP=+Vdd+LO; and
LOCPP=+Vdd+LO

Theoretically, a 3× higher swing can be achieved by increasing the supply voltage and increasing the power consumption by 9×. However, using the technique of clock boosting only the last transistor experiences the higher swing, so the total power consumption will be increased only by a factor of 4-5. In addition, owing to the limit of 2VDDfor the long-term reliability, supply voltage of a conventional driver cannot be increased to 3VDD. On the other hand, it is important to notice that despite of achieving a 3×VDDswing, none of the CMOS transistor cross the long-term reliability limit of 2×VDD. This clock boosting technique can be used to drive any of the passive mixers described above.

As described above in connection withFIG. 3, the transmission line should be quarter wave at the modulation frequency. Thus, while having a lower modulation frequency implies lower clocking power consumption, a lower modulation frequency means a longer transmission line and the area associated with it. While the electrical length of a lumped LC transmission line can be increased by increasing only the capacitance of the line with negligible increase in the area, doing so also changes the impedance of the transmission line.

When the gyrator is operated in an environment of Zo, it is intuitive to use a transmission line with impedance Zo so that there will be perfect matching. Typically, when we have an interface with Zo on one side and other impedance Zg on another side there will a mismatch.

As illustrated inFIGS. 18-24, the matching of the gyrator structure at the odd multiples of the modulation frequency will not be compromised by using a different impedance “Zg” for the transmission line in the gyrator. This happens in a very counter-intuitive way. As shown inFIGS. 19 and 23, when there is an impedance mismatch at odd multiples of the modulation frequency, multiple reflections at port 1 (between the Zo and Zg interface) and port 2 (between the Zg and Zo interface) add up in a destructive way leading to a perfect matching.

S2⁢1=((1-Γ2)⁢e-γ⁢l1+Γ2⁢e-2⁢γ⁢⁢l)
For a lossless case γ=jβ when

β⁢l=(2⁢N+1)⁢π2,
N=0, 1, 2, 3, . . .
S11=0; S21=(−1)N
Similarly:
S12=(−1)N+1j; S22=0
Thus, changing Zg does not affect the operation at center frequency and the structure acts as a gyrator for an Zg.

However, as shown inFIGS. 20, 21, 22, and 24, the contrast between the impedances “Zg/Zo” determines the bandwidth of this matching. For example, theoretically, the gyrator is matched over infinite bandwidth when Zg=Zo (as shown in the top row of the table ofFIG. 22where Zg−Zo−50 ohms). However, decreasing values of Zg will result in decreasing bandwidths as shown for example inFIG. 22(which is for a modulation frequency of 10 GHz). That is, for each lower value of Zg and each higher center frequency in the table ofFIG. 22, the Q value (which equals the center frequency (in the column heading) divided by 3 dB bandwidth) gets worse.

As shown inFIG. 20, the S11 parameter for the gyrator ofFIG. 19at a modulation frequency of 10 GHz shows no reflections (or virtually no reflections) at odd multiples of the modulation frequency (i.e., 10 GHz, 30 GHz, 50 GHz, 70 GHz, and 90 GHz), and strong reflections at other frequencies.

As shown inFIG. 21, the S21 parameter for the gyrator ofFIG. 19at a modulation frequency of 10 GHz shows no attenuation (or virtually no attenuation) at Zg equal to 49 ohms (whose line is straight across at 0 dB), and progressively larger attenuations at lower Zg impedances of 25 ohms, 5 ohms, and 1 ohm other than when at odd multiples of the modulation frequency (i.e., 10 GHz, 30 GHz, 50 GHz, 70 GHz, and 90 GHz), where there is no attenuation (or virtually no attenuation). Similarly, as shown inFIG. 24, the S21 parameter for the gyrator ofFIG. 23at a modulation frequency of 200 MHz shows no attenuation (or virtually no attenuation) at Zg equal to 100 ohms (whose line is straight across at 0 dB), and progressively larger attenuations at lower Zg impedances of 80 ohms, 60 ohms, 40 ohms, and 20 ohms other than when at odd multiples of the modulation frequency (i.e., 20 GHz, 30 GHz, 50 GHz, 70 GHz, and 90 GHz), where there is no attenuation (or virtually no attenuation).

In a circulator implementation in accordance with some embodiments, a 60 ohm differential transmission line can be used. For these embodiments, the −1 dB bandwidth of the gyrator can be 400 MHz, while the −1 dB bandwidth of the circulator is 200 MHz. Since the bandwidth of the gyrator is greater than the bandwidth of the circulator, the usage of mismatched transmission line does not affect the bandwidth of the circulator in these embodiments.

In some embodiments, a 60 ohm transmission line that is a quarter wave at 200 MHz can be used. A comparable transmission line with the similar chip area could be 100 ohm and a quarter wave at 333 MHz. Hence by compromising the bandwidth of the gyrator, the modulation frequency can be reduced to 200 MHz from 333 MHz. As a result of this, the power consumption of the switches can be reduced by 40% when used in a circulator built at 1 GHz. It is important to notice that, even if a gyrator is infinitely broadband, a circulator built using this gyrator is not infinitely broadband. So slightly relaxing the bandwidth of the gyrator should not compromise the bandwidth of the circulator built using the gyrator with a 60 ohm transmission line.

If one chooses, a transmission line can be implemented with a much lower characteristic impedance, consequently the modulation frequency, and the lower limit will be determined by the minimum bandwidth required by the system and additional loss added in the gyrator due to multiple reflections as shown inFIGS. 20, 21, 22, and 24.

Although single transmission lines are illustrated herein as having certain delays, such transmission lines can be implemented as two or more transmission lines having the same total delay.

Although the disclosed subject matter has been described and illustrated in the foregoing illustrative implementations, it is understood that the present disclosure has been made only by way of example, and that numerous changes in the details of implementation of the disclosed subject matter can be made without departing from the spirit and scope of the disclosed subject matter, which is limited only by the claims that follow. Features of the disclosed implementations can be combined and rearranged in various ways.