## Description

# A System of Two Coupled Oscillators With a Continuously Controllable Phase Shift

**Existing System:**

COUPLED oscillator systems have been used in numerous applications. A classic example is the LC quadrature oscillator widely used in image reject transceivers, where two identical LC oscillators are asymmetrically coupled so that they oscillate with a relative ±90◦ phase shift with respect to each other. More recently, the nonlinear dynamics of coupled oscillators was used to demonstrate a novel way of frequency tuning in a closed loop of unidirectionally coupled oscillators, which avoided using lossy varactors inside oscillator’s tanks. Coupled oscillators have also been used in neuromorphic associative memory and pattern recognition applications. In these neuromorphic computation paradigms, information is typically encoded in the relative phase shifts between coupled oscillators and having a reliable mechanism for controlling the phase shift between oscillators with high precision is critical.

Using the untapped millimeter frequency band at 28-38 GHz is widely considered to be the viable solution for accommodating the large channel bandwidths required for 5G wireless communications. Historically, millimeter wave frequencies were not used for cellular communications due to concerns for high propagation loss and low power levels generated by CMOS devices as compared to RF frequencies. However, shrinking cell sizes and advances in CMOS technology has made mm-Wave communications feasible provided that adaptive beamforming is used to compensate for the additional propagation losses.

In order to reduce the cost and complexity of the conventional phased array architectures, a phase-shifter-less approach to beamforming has been introduced by York and Itoh . As shown in Fig. 2, the basic idea is to use the induced phase shifts in injection-locked oscillators to generate the desired phase progression patterns in an array of local oscillators and therefore eliminate the explicit phase shifters involved in the conventional phased array design. More specifically, Adler’s classic analysis of injection locking predicts that when a local oscillator with a free-running frequency of ω0 is injection locked to a master oscillator with a frequency of , there will be a finite phase shift, φ, between the two oscillators equal to: Ref eq 1 & 2.

Equations (1) and (2) point to a couple of drawbacks with this approach. Firstly, from (1) we can see that there is a nonlinear interdependence between direction and the frequency of the radiated beam. Secondly, (2) shows that there is a direct trade-off between the locking range, hence directional resolution of the beam, with quality factor of the local oscillators. In general, oscillators with low Q are less efficient and have poor phase noise performance. The latter factor becomes particularly significant at the edges of the locking range (i.e. for generating φ close to ±π/2) since then the phase noise of the local oscillator no longer follows that of the master oscillator and approaches the free running phase noise dictated by Q.

As shown in Fig. 3, an APO based phased array provides a new alternative to traditional phased array architectures. A general advantage of coupled oscillator phased arrays is in the scalability of layout for larger arrays as each antenna is fed by a designated, nearby VCO and hence the long interconnectsand the complex feed networks in traditional systems are eliminated. Our APO based architecture has the added benefit of eliminating phase shifters to reduce size, cost and complexity of such systems. The desired phase shifts between oscillators are directly constructed from the naturally available phase relationships between different stages of three stage LC ring oscillators and obviate the need for any explicit phase shifting mechanism in the coupling paths.

It should be emphasized that the current work addresses only the design of the APO sub-block, enclosed in the dotted rectangle in Fig. 3 and serves as a proof of concept for the proposed APO based phased array architecture. Our simulation results for 1 × 4 and 2 × 2 phased array structures at millimeter wave frequencies confirm that the underlying phase shifting mechanism continues to work for such systems. However, a careful and detailed design of the complete APO phased array at millimeter wave frequencies will be the focus of our future work.

**Disadvantages:**

- High insertion loss.
- Large in size.
- Poor phase noise performance.

**Proposed System:**

In a recent Methodology of Coupled Oscillator system which have been a numerous applications. Here this work will present a Coupled Oscillator with novel generalization of quadrature oscillators (QVCO) its only generate a phase output at quadrature phases, which present as a Aribitrary phase oscillators (APO) it have a ability to generate any desired phase output. The propsoed structure of this work which present a novel coupling mechanism to generate arbitrary phas shifts between two coupled oscillators without the need of an explicit phase shifter. Here, the proposed work will integrated and verified net list simulation of 130nm at 0.9V supply voltage and 45nm at 0.7V supply voltage with 5GHz Clock Frequency range. The APO structure can be used in designing novel coupled-oscillator-based phased arrays for 5G wireless communications.

**Coupled Oscillators**

Many important physics systems involved coupled oscillators. Coupled oscillators are oscillators connected in such a way that energy can be transferred between them. The motion of coupled oscillators can be complex, and does not have to be periodic. However, when the oscillators carry out complex motion, we can find a coordinate frame in which each oscillator oscillates with a very well defined frequency. A solid is a good example of a system that can be described in terms of coupled oscillations. The atoms oscillate around their equilibrium positions, and the interaction between the atoms is responsible for the coupling. To start our study of coupled oscillations, we will assume that the forces involved are spring-like forces.

**LC Oscillators**

Oscillator convert a DC input (the supply voltage) into an AC output (the waveform), which can have a wide range of different wave shapes and frequencies that can be either complicated in nature or simple sine waves depending upon the application. Oscillators are also used in many pieces of test equipment producing either sinusoidal sine waves, square, saw tooth or triangular shaped wave forms or just a train of pulses of a variable or constant width. LC Oscillator are commonly used in radio-frequency circuits because of their good phase noise characteristics and their ease of implementation. An Oscillator is basically an Amplifier with “Positive Feedback”, or regenerative feedback (in-phase) and one of the many problems in electronic circuit design is stopping amplifiers from oscillating while trying to get oscillators to oscillate.

Oscillators work because they overcome the losses of their feedback resonator circuit either in the form of a capacitor and inductor or both in the same circuit by applying DC energy at the required frequency into this resonator circuit. In other words, an oscillator is a an amplifier which uses positive feedback that generates an output frequency without the use of an input signal. Thus Oscillators are self sustaining circuits generating an periodic output waveform at a precise frequency and for any electronic circuit to operate as an oscillator, it must have the following three characteristics.

**Quadrature Oscillators**

The quadrature oscillator is another kind of phase shift oscillator. The difference is that the quadrature oscillator uses an op amp integrator to obtain a full 90° phase shift from a single RC segment, and still produce a usable output voltage. Because of that 90° phase shift, we only need two op amps to produce both sine and cosine wave outputs, as shown in the circuit to the right. At the same time, however, we do still need three RC segments as shown. Frequency of operation will be ω = 2πf = 1/RC if all components are matched.

** **There are a number of variations on this circuit, but the basic operation is still the same. Amplitude control can be an issue, and too high an amplitude leads to distortion of the waveform. To limit the output amplitude, some circuits use a pair of back-to-back Zener diodes or some equivalent circuit to clip the signal fed back from the Cosine output to the Sine integrator. Because all RC segments are also low-pass filters, the distortion produced by the clipping action is significantly reduced, and the output signals are both good quality sine and cosine waves. At the same time, if the loop gain is insufficient, oscillations will cease, or will not start when power is applied. To assure sufficient gain, resistor R_{1} is often made slightly smaller than R.

**Overview Of The APO Structure**

The simplified schematic of our proposed APO structure is shown in Fig. 6. The system consists of two identical, three stage LC oscillators that are connected through a “multi channel” coupling network. The “coupling channels” that are distinguished by different colors in Fig. 6, connect different sets of nodes in the two oscillators and their coupling strengths (conductance of the coupling transistors in the middle) are tunable with analog voltages Va, Vb, Vc. We have distinguished the two oscillators by numbers “1” and “2” and the three stages in each oscillator by letters “A”, “B”, and “C” so that different nodes of the oscillators are labeled as “1A”, ”2A” and so forth. Simple voltage dividers formed by C1, C2 capacitive pairs along with the DC biasing resistors RBI AS , attenuate the oscillator’s large signals before applying them to the source/drain terminals of the coupling transistors in order to guarantee a linear, small signal operation of the coupling transistors. The attenuated signal nodes are indicated by lower alphabet letters so that for example “1a” is the attenuated version of “1A”. Finally, let us also label the coupling channels by Ga, Gb and Gc. By convention, the subscript in the name of each coupling channel, that is x in Gx , is chosen so to indicate that nodes 2x and 1a are connected in the Gx channel. In order to simplify our notation, we will also refer to the controllable conductances of these coupling channels by the same letters Ga, Gb and Gc in the rest of this paper since the context should be enough to resolve any confusion. With these notations, we can symbolically describe the coupling channels by listing all the connections that each one of them provide between the two oscillators:

** Advantages:**

- Reduce insertion loss.
- Reduce size by eliminating phase shifter.
- Better phase noise performance.

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# A System of Two Coupled Oscillators With a Continuously Controllable Phase Shift

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