PRIORITY CLAIM 
       [0001]    This application claims priority to the following U.S. Provisional Patent Application: 
         [0002]    U.S. Provisional Patent Application No. 60/862,170, entitled “INTERLEAVED NON-LINEAR TRANSMISSION LINES FOR SIMULTANEOUS RISE AND FALL TIME COMPRESSION,” Attorney Docket No. ANRI-08080US0, filed Oct. 19, 2006. 
     
    
     TECHNICAL FIELD 
       [0003]    The present invention relates generally to generation of microwave and millimeter wave signals, clock waveforms and delayed signals. 
       BACKGROUND OF THE INVENTION 
       [0004]    Non-linear transmission lines support shock waves and electrical solitons, as has been known theoretically and demonstrated experimentally.  FIG. 1A  shows a periodic structure  100  made up of a non-linear waveguide comprising a transmission line consisting of a pair of conductors  102 , 104  loaded with varactor diodes  106  implementable in gallium arsenide (GaAs) technology and demonstrated to compress the fall time of a sinusoidal microwave signal. The varactor diodes  106  are separated by plurality of transmission line segments  112  of approximately equal line lengths or period d. A DC power supply  116  provides reverse bias to the varactor diodes  106 . A signal generator  108 , one node of which is grounded, supplies a generally sinusoidal input voltage signal  190  with a typical waveform as shown in  FIG. 1B  to the non-linear transmission line. The signal generator  108  has source impedance represented by a resistor  114 . A load  110  is connected to receive a resultant output signal  192  shaped by the varactor-loaded transmission line, a typical waveform of which is shown in  FIG. 1B . 
         [0005]      FIG. 2A  shows a periodic structure  200  made up of a non-linear waveguide comprising a transmission line consisting of a pair of conductors  202 , 204  loaded with varactor diodes  206  implemented in gallium arsenide (GaAs) technology and demonstrated to compress the rise time of a sinusoidal microwave signal. The varactor diodes  206  are separated by plurality of transmission line segments  212  of approximately equal line lengths or period d. A DC power supply  218  provides reverse bias to the varactor diodes  206 . An input signal  290  and resultant output signal  292  are shown in  FIG. 2B . 
         [0006]    U.S. Pat. No. 5,789,994 to Case et al. teaches a non-linear waveguide employing a pair of transmission lines loaded with anti-parallel varactor diodes used to simultaneously compress the rise and fall times of a sinusoidal signal. The conversion efficiency of the circuit is lower than that of a purely reactive non-linear transmission line because the anti-parallel arrangement of one set of varactor diodes is reverse biased (reactive non-linearity) while the other set of varactor diodes is forward biased (resistive non-linearity). 
         [0007]    In another approach, heterostructure barrier varactor diodes (HBV) having a symmetric C-V characteristic are used to generate odd-frequency harmonics (i.e. a square wave). However, self heating caused by the conduction current through the bulk of the varactor diodes results in reduced conversion efficiency. In addition, the unconventional epitaxy of HBV diodes can make their integration with other common processes (e.g. PHEMT, HBT) difficult. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0008]    Further details of embodiments of the present invention are explained with the help of the attached drawings in which: 
           [0009]      FIG. 1A  is a circuit diagram of a periodic non-linear transmission line for fall-time compression in accordance with the prior art. 
           [0010]      FIG. 1B  is an exemplary plot of an input signal passed through the non-linear transmission line of  FIG. 1A , and a resulting output signal. 
           [0011]      FIG. 2A  is a circuit diagram of a periodic non-linear transmission line for rise time compression in accordance with the prior art. 
           [0012]      FIG. 2B  is an exemplary plot of an input signal passed through the non-linear transmission line of  FIG. 2A , and a resulting output signal. 
           [0013]      FIG. 3A  is a circuit diagram of an embodiment of a periodic non-linear transmission line in accordance with the present invention for simultaneous rise and fall time compression. 
           [0014]      FIG. 3B  is a plot of an input signal passed through the periodic non-linear transmission line of  FIG. 3A , and a resulting output signal. 
           [0015]      FIG. 4A  is a simplified circuit diagram of a portion of an embodiment of a non-linear transmission line as shown in  FIG. 3A . 
           [0016]      FIG. 4B  is the simplified circuit diagram of  FIG. 4A  expressed using alternative structures. 
           [0017]      FIG. 5  is an equivalent circuit expressing at least a portion of the circuit of  FIG. 4B . 
           [0018]      FIG. 6A  is an embodiment of a co-planar-waveguide chip layout in accordance with the present invention for defining the non-linear transmission line of  FIG. 3A . 
           [0019]      FIG. 6B  is an expanded view of the input and output of the co-planar-waveguide chip layout of  FIG. 6A . 
           [0020]      FIG. 7  is an embodiment of a test setup for measuring an output signal of an interleaved co-planar-waveguide type of non-linear transmission line in accordance with the present invention. 
           [0021]      FIG. 8A  is a plot of output power of second and third harmonics for a +24 dBm input signal measured using the test setup of  FIG. 7 . 
           [0022]      FIG. 8B  is a plot of output power of fourth and fifth harmonics for a +24 dBm input signal measured using the test setup of  FIG. 7 . 
           [0023]      FIG. 9A  is a plot of output power of second and third harmonics for a +28 dBm input signal measured using the test setup of  FIG. 7 . 
           [0024]      FIG. 9B  is a plot of output power of fourth and fifth harmonics for a +28 dBm input signal measured using the test setup of  FIG. 7 . 
           [0025]      FIG. 10  is a plot of output voltage waveforms for different reverse-bias voltages measured using a sampling oscilloscope. 
           [0026]      FIG. 11A  is a plot of output voltage and a first normalized input waveform measured using a sampling oscilloscope. 
           [0027]      FIG. 11B  is a plot of output voltage and a second normalized input waveform measured using a sampling oscilloscope. 
           [0028]      FIG. 11C  is a plot of output voltage and a third normalized input waveform measured using a sampling oscilloscope. 
       
    
    
     DETAILED DESCRIPTION 
       [0029]    Embodiments of nonlinear waveguides in accordance with the present invention can achieve simultaneous rise and fall time compression by interleaving a portion of a fall time compression circuit and a portion of a rise time compression circuit while providing a first reverse bias to rise compression varactor diodes  307  and a second reverse bias to fall compression varactor diodes  306  by way of two separate DC paths  316 , 318 . The resulting interleaved structure is a reactive device that results in conversion efficiency improvements over typical non-linear waveguides. Referring to  FIG. 3A , an embodiment of a non-linear waveguide in accordance with the present invention is shown comprising a transmission line including a pair of conductors  302 , 304  loaded with varactor diodes  306 , 307  arranged in an anti-parallel fashion. The varactor diodes  306 , 307  are separated by a plurality of transmission line segments  312  of approximately equal line lengths D. Non-linear transmission lines loaded periodically with varactor diodes at regular intervals d are said to be periodic. 
         [0030]    The cell length d defines the pitch or periodicity of the interleaved nonlinear transmission line. A signal generator  308 , one node of which is grounded, supplies a signal to the interleaved non-linear transmission line. The signal generator  308  has source impedance represented by a resistor  314 . A load  310  is connected to receive a resultant output signal. When driven by a large input signal  390 , for example as shown in  FIG. 3B , the non-linear waveguide compresses simultaneously the rise and fall times of the generally sinusoidal input signal  390  to produce an output signal such as shown in  FIG. 3B . The amount of compression is dependent on the amplitude of the input signal, the number of varactor-diode sections and spacing between the varactor-diode sections, attenuation along the interleaved non-linear transmission line, and DC-bias values. Embodiments of waveguides in accordance with the present invention can enable one or more of (for example) conversion of a sinusoidal signal into a clock signal or equivalently into odd harmonics, simultaneous enhancement of the rise and fall times of a clock or data signal, and simultaneous variation of the rise and fall times of a signal by varying the signal&#39;s amplitude and the DC bias. 
         [0031]    In other embodiments, the plurality of transmission line segments can be separated by non-equal line lengths. For example, high-frequency performance of a nonlinear transmission line can be improved upon by progressively decreasing the pitch between varactor diodes from the input to the output, thereby increasing the output Bragg frequency (also referred to herein as cutoff frequency, F c ) of the periodic structure or circuit as taught in U.S. Pat. No. 5,014,018. However, decreasing spacing between varactor diodes changes the large-signal characteristic impedance of the nonlinear transmission line and must be compensated for by scaling the varactor-diode capacitance. The large-signal characteristic impedance is preferably constrained to approximately 50 ohms in a preferred embodiment (although in other embodiments in accordance with the present invention different characteristic impedances can be used to suit specific applications). In such a case, the cutoff frequency is limited mainly by spacing between adjacent varactor diodes and by lithographic constraints on the minimum junction area for the varactor. Adjacent varactor diodes are spaced far enough apart so as to result in low electromagnetic coupling between them. Non-linear transmission lines having transmission line segments of varying length can be said to be non-periodic. 
         [0032]    In still other embodiments, the cutoff frequency of the nonlinear transmission line or waveguide can increase in blocks of sections. Thus, each block can contain a plurality of varactors. In the first block, the varactor diodes will have a first junction area and a first spacing. In the second block, the junctions will all be the same size but smaller than the size of junctions in the first section. Further, the spacing between the varactor diodes in the second section will be closer in proportion to the decrease in the junction area so as to maintain the characteristic impedance of that section at approximately 50 ohms. This pattern of ever-decreasing junction area and spacing between the varactor diodes in each block can be repeated, for example, until an appropriate length for the transmission line is achieved that results in a required electrical performance. 
         [0033]    When driven by a small input signal, the non-linear waveguide can be used in an embodiment as a variable-delay line or phase shifter having a broad instantaneous bandwidth. Instantaneously broadband variable-delay lines can be used in myriad different circuits, for example as phase detectors for clock and data recovery, broadband wireless communications, phased arrays, etc. 
         [0034]      FIG. 4A  illustrates a simplified circuit diagram of a portion of an embodiment of a non-linear transmission line as shown in  FIG. 3A  for compressing the fall time and the rise time of a sinusoidal signal. The circuit of  FIG. 4A  can be expressed as shown in  FIG. 4B , wherein the diode is expressed by way of relationships based on equations (1)-(3): 
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         [0035]    An equivalent circuit for the circuit of  FIG. 4B  is illustrated in  FIG. 5 , and is derived by way of equations (4)-(7), below. 
         [0000]        C   j1   =C   j ( V   D1 )= C   j ( VR   F ( t )− V   DC1 )=C j ( V   RF ( t )− V   0 )  (4) 
         [0000]        C   j2   =C   j ( V   D2 )= C   j (− V   RF ( t )+(− V   DC2   +V   DC1 ))= C   j (− V   RF ( t )− V   0 )  (5) 
         [0000]      − V   0   &lt;V   RF ( t )&lt; V   0   &lt;V   BR             i→i   s             G ( V )→0  (6) 
         [0000]        C   eq   =C   j1   ++C   j2   =C   j ( V   RF )( t )− V   0 )+ C   j (− V   RF ( t )− V   0 )  (7) 
         [0036]    An embodiment of a commensurate non-linear co-planar waveguide  400  employing the arrangement described above is illustrated in  FIGS. 6A and 6B , and includes a sixteen-section GaAs co-planar-waveguide chip layout of the interleaved circuit in which each section is made up of two hyperabrupt Schottky varactor diodes  406 , 407  for a total of 32 varactors. The rise-time compression varactor diodes  407  are electrically connected with a reverse DC bias through a capacitor  430  by way of a pair of very-high-impedance traces  418 . As shown, the traces  418  have a step geometry and a desired inductance. The traces  418  are isolated from the ground traces by an insulating under-layer, or some other barrier layer. DC bias for fall-time compression varactor diodes  406  is applied between the center conductor trace  402  and the ground trace  404  by way of a bias tee  442  (as shown in  FIG. 7 ). The ground traces are connected by a plurality of bridges  440  spanning the center conductor  402 . While the waveguide is shown having two ground traces and a center conductor trace between the ground traces, the structure is defined as such to comport with current standards for design of co-planar-waveguides. In other embodiments, the waveguide can have some other chip layout. For example, in an embodiment, the waveguide can have a single ground trace. 
         [0037]    Conductor loss for a coplanar waveguide transmission line can be reduced by elevating the center conductor  402  above the substrate surface as taught in U. Bhattacharya et al., IEEE Microwave and Guided Wave Letters, vol. 5, No. 2, February 1995, pp. 50-52. Further, shock-wave coupling to surface-wave modes is reduced by elevating the center conductor  402  or all conductors  402 , 404  above the substrate surface as taught in U.S. Pat. No. 6,894,581. The elevated center conductor  402  is supported by means of conducting posts, or may be backed by a low-loss dielectric such as polyimide, BCB (benzo-cyclo-butene), or silicon nitride. Reduced coupling is further achieved by selecting properly the thickness of the semiconductor substrate. The reduced coupling enhances the high-frequency performance of nonlinear-transmission-line-based circuits. High-frequency harmonics can be generated in an efficient way by reducing the effect of conductor loss and loss to surface-wave modes. 
         [0038]      FIG. 7  illustrates an experimental setup for measuring an output signal of an embodiment of an interleaved non-linear transmission line such as that shown in  FIG. 6 . As shown, a calibrated spectrum analyzer  414  is connected as a load to the non-linear waveguide  400  having rise compression (not shown) provided with a reverse bias from a first DC power supply  418  and fall compression varactor diodes provided with a reverse bias from a second DC power supply  416 . As shown, a signal from a signal generator  408  has source impedance represented by a resistor  414 . The input signal is amplified by a power amplifier  420  and passed through a low-pass filter  422  before being sent to the non-linear waveguide  400 . An experimental setup as shown in  FIG. 7  and another based on a sampling oscilloscope were employed to measure an ability of the interleaved non-linear waveguide  400  to perform one or more of converting a sinusoidal signal into a clock signal or equivalently into odd harmonics, enhancing simultaneously the rise and fall times of a clock or data signal, and varying simultaneously the rise and fall times of a signal by varying the signal&#39;s amplitude. 
         [0039]      FIGS. 8A-11C  are plots communicating measurements of an output signal given an input signal indicated on the plot provided to the test set-up of  FIG. 7 . 
         [0040]    The foregoing descriptions of the present invention have been presented for purposes of illustration and description. They are not intended to be exhaustive or to limit the invention to the precise forms disclosed. Many modifications and variations will be apparent to practitioners skilled in this art. The embodiments were chosen and described in order to best explain the principles of the invention and its practical application, thereby enabling others skilled in the art to understand the invention for various embodiments and with various modifications as are suited to the particular use contemplated. It is intended that the scope of the invention be defined by the following claims and their equivalents.
A non-linear waveguide comprises a transmission line including a first conductive line and a second conductive line; a first bias voltage supply connected with the transmission line; and one or more pairs of diodes connected between the first conductive line and the second conductive line, the one or more pairs of diodes including: a first diode having an anode connected with the first conductive line and a cathode connected with the second conductive line; a second diode having a cathode connected with the first conductive line and an anode connected with the second conductive line; and a second bias voltage supply connected between the anode of the second diode and the second conductive line.