Abstract:
A low-loss directional bridge for measuring propagated signals from a source device to a load device or from a load device to a source device, where both the source device and the load device are in signal communication with the low-loss directional bridge. The low-loss directional bridge may include a first bridge circuit network and a first sensing element in signal communication with the first bridge circuit network. The first sensing element may produce a first measured signal that is proportional to the propagated signals. Additionally, the first bridge circuit network may include a first, a second, and a third impedance element in signal communication with the source device and the first sensing element.

Description:
CROSS REFERENCE TO RELATED APPLICATION(S)  
       [0001]     This application is a continuation-in-part of U.S. patent application Ser. No. 11/071,670 filed Mar. 1, 2005, titled “An Integrated Directional Bridge,” which is incorporated into this application in its entirety by reference. 
     
    
     BACKGROUND OF THE INVENTION  
       [0002]     Radio frequency (“RF”), microwave, and millimeter(“mm”)-wave applications of the present day and the future have a constant need for lower weight, volume, power consumption and cost together with greater functionality, frequency of operation and component integration. Examples of such applications include wireless handsets for messaging, wireless Internet services for e-commerce, and wireless data links such as Bluetooth.  
         [0003]     Typically, telecommunication devices, and electronic equipment in general, include numerous types of electronic components and circuits including directional couplers and directional bridges. In general, directional couplers and directional bridges are electronic devices utilized in RF, microwave, and mm-wave signal routing for isolating, separating, or combining signals. Directional couplers and bridges also find use in a variety of measurement applications: power monitoring, source leveling, isolation of signal sources, and swept transmission and reflection measurements. Typically, directional couplers are utilized as impedance bridges for microwave and mm-wave measurements and for power monitoring.  
         [0004]     Directional couplers and directional bridges (generally known as “directional circuits”) are usually three-port or four-port devices/circuits that have a signal input port (from a source) and a signal output port (to a load) and at least one coupled port whose output is proportional to either the incident wave (from the source) or the reflected wave (from the load). It is appreciated by those skilled in the art that it is common practice in RF, microwave, and mm-wave engineering to consider an electrical signal in an electronic circuit/device as the sum of an incident and a reflected traveling wave to and from, respectively, a load, or from and to, respectively, a source, relative to a characteristic impedance Z 0  of the electronic circuit/device (typically about 50 ohms). A directional circuit generally separates a transmitted signal into the detection circuit or coupled port based on the direction of the signal propagation. There are many uses for these directional circuits including network analysis and monitoring the output signal levels of a traveling wave incident on a load.  
         [0005]     At present, there are numerous approaches to implementing a directional circuit. One example approach is to implement a distributed directional coupler as a device that has a physical length over which two transmission lines couple together electromagnetically or that utilizes the phase shift along a length of transmission line. In the distributed element model or transmission model of electronic circuits, it is assumed that each circuit element is finite, as opposed to infinitesimal, and the wires connecting elements are not perfect conductors, i.e., they have impedance. Another example approach (known as a directional bridge) may utilize lumped elements that may include transformers and resistors. In the lumped element model of electronic circuits, the simplifying assumption is made that each element is an infinitesimal point in space, and that the wires are perfect conductors. Thus, in this model the “lumped circuit elements” are the resistor, the capacitor, the inductor, and the transmission line, each of which may be lumped into a single point.  
         [0006]     In  FIG. 1 , an example approach of an implementation of a known directional bridge circuit  100  is shown. The directional bridge circuit  100  may include three ports such as a signal input port (“port A  102 ”), a signal output port (“port B  104 ”), and at least one coupled port (“port C  106 ”). The directional bridge circuit  100  may be in signal communication with a signal source  108  via signal source impedance (“Z source ”)  110 , and a load having a load impedance (“Z load ”)  112 . As an example of operation, the directional bridge circuit  100  may be utilized to unequally split the signal  116  flowing in from the source at port A  102  while simultaneously fully passing the signal  114  flowing in from the opposite direction from the load  112  into port A. Ideally the signal  116  flowing in from the source at port A  102  will pass to the coupled port C  106  and appear as coupled signal  118 . Similarly, an input signal  120  at port C  106  would be coupled fully to port A  102 . However, port B  104  and port C  106  are isolated in that any signal  114  flowing into port B  104  will not appear at port C  106  but will propagate through to port A  102 . Additionally, port B  104  is isolated from port C  106  because any signal  120  from port C  106  will flow to port A  102 , and not to port B  104 .  
         [0007]     In  FIG. 2 , a block diagram of an example of an implementation of an integrated directional bridge circuit  200  utilizing a basic directional circuit topology is shown in normal configuration. The directional bridge circuit  200  may be in signal communication with a signal source  202  having a signal source impedance (“Z source ”)  204  and a load having a load impedance (“Z load ”)  206  via signal paths  208  and  210 , respectively. The directional bridge circuit  200  may include impedance elements Z 1    212 , Z 2    214 , Z 3    216 , Z 4    218 , and Z 5    220 , and sensing element  222 . In the example directional circuit topology, the signal source impedance Z source    204  is in signal communication with both impedance elements Z 1    212  and Z 4    218 . The load impedance Z load    206  is in signal communication with both impedance elements Z 1    212  and Z 2    214 . The sensing element  222  is in signal communication with both Z 4    218  and Z 5    220  at node  224  having a node voltage V 4 . Similarly, the sensing element  222  is also in signal communication with both Z 2    214  and Z 3    216  at node  226  having a node voltage V 3 . Both Z 5    220  and Z 3    216  are in signal communication with a common ground  228 .  
         [0008]     The impedance elements Z 1    212 , Z 2    214 , Z 3    216 , Z 4    218 , and Z 5    220  may be either reactive impedance elements, real impedance elements (i.e., resistive elements), or combinations of real and reactive elements based on the frequency range of operation of the directional bridge circuit  200 . The sensing element  222  (which may be a DC-coupled differential amplifier with a high common mode rejection ratio, or a Gilbert Cell mixer with differential RF input) senses the difference in voltage between node voltages V 3  and V 4  and produces a difference signal  230  of the voltage difference between node voltages V 3  and V 4  in both magnitude and phase, and characteristic impedance Z 0  of the directional coupling circuit  200  may be expressed as:  
               Z   0     =         Z   1     ⁡     (       Z   2     +     Z   3       )           Z   1     +     Z   2     -         Z   3     ⁢     Z   4         Z   5                   (   2   )             
 
         [0009]     As an example of operation, it is appreciated by those skilled in the art that the amplified difference signal  230  may be proportional to either the incident voltage signal (“V incident ”)  232  from the directional bridge circuit  200  to Z load    206  or the reflected voltage (“V reflected ”)  234  from Z load    206  to the directional bridge circuit  200 . It is also appreciated that a passive load Z load    206  produces V reflected    234  by reflecting V incident    232  and that the reference impedance Z 1  for V incident    232  and V reflected    234  is also given by equation (2). Additionally, it is appreciated that V reflected    234  may be generated by Z load , if Z load  is an active device.  
         [0010]     If the sensing element  222  is a differential amplifier, such as an operational amplifier connected between the nodes  224  and  226 , the proportional factor (“k”) is equal to the amplifier gain of the differential amplifier multiplied by the coupling factor of the directional bridge circuit  200 . It is appreciated that based on the values of the impedance elements Z 1    212 , Z 2    214 , Z 3    216 , Z 4    218 , and Z 5    220 , the directional circuit  200  may be configured to produce an amplified difference signal  230  that is proportional to either V incident    232  or V reflected    234 .  
         [0011]     Unfortunately, directional couplers made using the distributed element model have the disadvantage that they are typically too large to be practical for an integrated circuit (“IC”) except at very high frequencies. And at low frequencies approaching direct current (“DC”), they also are typically too large to be practical for many electronic instruments. As an example, directional couplers are usually limited by size limitations to low frequency operation of about 10 megahertz (“MHz”) in most electronic devices.  
         [0012]     Attempts to solve this problem include utilizing directional bridges because directional bridges typically operate at lower frequencies than directional couplers. However, while directional bridges may typically operate in the kilohertz (“KHz”) frequency range, they still unfortunately do not operate at low frequencies approaching DC. Additionally, similar to known directional couplers, known directional bridges are not suitable for integration on ICs because directional bridges generally utilize transformers that are difficult to implement with known IC technologies, particularly at low frequencies. Moreover, broadband instrument grade directional couplers and conventional directional bridges are typically implemented with expensive precision mechanical parts and assemblies and typically require hand assembly and adjustment.  
         [0013]     Therefore, there is a need for a new directional circuit/device capable of operating continuously from DC up to high frequencies in the mm-wave range while being simple to integrate with known IC technologies.  
       SUMMARY  
       [0014]     A low-loss directional bridge circuit for measuring propagated signals from a source device to a load device and from the load device to the source device, where both the source device and the load device are in signal communication with the directional bridge circuit, is disclosed. The low-loss directional bridge circuit may include lumped elements in a conventional directional bridge circuit where impedances are replaced with impedances that are very large, thus approximating an open circuit, or very small, thus approximating a short circuit. The directional bridge circuit may also include resistive elements and reactive elements that result in a low-insertion-loss directional bridge circuit.  
         [0015]     In an example of an implementation of the low-loss directional bridge in accordance with the invention, the first bridge circuit network may include a first impedance element in signal communication with both the source device and the first sensing element at a first node and a second impedance element in signal communication with the first impedance element at a second node and in signal communication with the first sensing element at a third node. Additionally, the first bridge circuit network may include a third impedance element in signal communication with both the second impedance element and the first sensing element at the third node. The first measured signal may be produced by the first sensing element in response to detecting a difference in voltage between a first voltage at the first node and a second voltage at the third node.  
         [0016]     The low-loss directional bridge may further include a second bridge circuit network and a second sensing element in signal communication with the second bridge circuit network and both the first impedance element and the second impedance element at the second node, wherein the second sensing element produces a second measured signal that is proportional to the propagated signals. The second bridge circuit network may include a fourth impedance element in signal communication with both the first impedance element and the first sensing element at the first node and in signal communication with the second sensing element at a fourth node, and a fifth impedance element in signal communication with both the fourth impedance element and the second sensing element at the fourth node. The second measured signal may be produced by the second sensing element in response to detecting a difference in voltage between a third voltage at the fourth node and a fourth voltage at the second node.  
         [0017]     Alternatively, the low-loss directional bridge may further include a second bridge circuit network and a second sensing element in signal communication with the second bridge circuit network and both a fourth impedance element and the load device at a fourth node, wherein the second sensing element produces a second measured signal that is proportional to the propagated signals. The second bridge circuit network may include a fifth impedance element in signal communication with both the first impedance element and the fourth impedance element at the second node and in signal communication with the second sensing element at a fifth node and a sixth impedance element in signal communication with both the fourth impedance element and the second sensing element at the fifth node. The second measured signal may be produced by the second sensing element in response to detecting a difference in voltage between the first voltage at the second node and a third voltage at the fourth node.  
         [0018]     A low-loss directional bridge may be implemented in various configurations using lumped two-terminal elements, which may include resistors, capacitors, inductors, and transmission lines. As an example, a low-loss directional bridge network may be implemented having a low-pass configuration, in which case the first impedance element may include a series inductor, the second impedance element may include a shunt resistor, and the third impedance element may include a shunt capacitor. In the case of the low-pass configuration, the low-loss directional bridge may also include series matching capacitors.  
         [0019]     Alternatively, the directional bridge may be implemented having a high-pass configuration, in which case the first impedance element may include a series capacitor, the second impedance element may include a shunt resistor, and the third impedance element may include a shunt inductor. In the case of the high-pass configuration, the low-loss directional bridge may also include series matching inductors. In yet another alternative, the directional bridge may be implemented having a bandpass configuration, in which case the first impedance element may include a series resonator, which may include a capacitor and an inductor in series, the second impedance element may include a shunt resistor, and the third impedance element may include a parallel resonator, which may include a capacitor and an inductor in parallel.  
         [0020]     Additionally, a low-loss directional bridge may be implemented by cascading a plurality of directional bridge networks and forming a dual-directional bridge, which may have, by way of example, a low-pass low-pass configuration, a high-pass low-pass configuration, a low-pass high-pass configuration, or any other combination.  
         [0021]     Additionally, the low-loss directional bridge may be implemented utilizing various devices as the sensing element. As an example, a low-loss directional bridge may be implemented using a detector diode or peak-to-peak detector diodes, as well as differential amplifiers.  
         [0022]     Other systems, methods and features of the invention will be or will become apparent to one with skill in the art upon examination of the following figures and detailed description. It is intended that all such additional systems, methods, features and advantages be included within this description, be within the scope of the invention, and be protected by the accompanying claims. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0023]     The invention can be better understood with reference to the following figures. The components in the figures are not necessarily to scale, emphasis instead being placed upon illustrating the principles of the invention. In the figures, like reference numerals designate corresponding parts throughout the different views.  
         [0024]      FIG. 1  shows a block diagram of an example of an implementation of a known directional bridge circuit.  
         [0025]      FIG. 2  shows a block diagram of an example of an implementation of a known directional bridge circuit in a normal configuration.  
         [0026]      FIG. 3  shows a block diagram of an example of an implementation of an integrated low-loss directional bridge circuit utilizing a directional circuit topology in accordance with the invention.  
         [0027]      FIG. 4  shows a block diagram of an example of an implementation of an integrated low-loss directional bridge circuit in a low-pass configuration in accordance with the invention.  
         [0028]      FIG. 5  is a block diagram of an example of an implementation of an integrated low-loss directional bridge circuit in a high-pass configuration in accordance with the invention.  
         [0029]      FIG. 6  shows a block diagram of an example of an implementation of an integrated low-loss directional bridge circuit in a bandpass configuration in accordance with the invention.  
         [0030]      FIG. 7  shows a block diagram of an example of an implementation of an integrated low-loss directional bridge circuit in a low-pass configuration with series matching capacitors in accordance with the invention.  
         [0031]      FIG. 8  shows a block diagram of another example of an implementation of an integrated low-loss directional bridge circuit in a high-pass configuration with series matching inductors in accordance with the invention.  
         [0032]      FIG. 9  shows a block diagram of another example of an implementation of an integrated low-loss directional bridge circuit in a low-pass configuration with a parasitic series resistor in accordance with the invention.  
         [0033]      FIG. 10  shows a block diagram of an example of an implementation of an integrated low-loss directional bridge utilizing a frequency-compensated directional bridge topology having a detector diode in accordance with the invention.  
         [0034]      FIG. 11  shows a block diagram of an example of an implementation of an integrated low-loss directional bridge that utilizes a peak detector diode as a sensing element in accordance with the invention.  
         [0035]      FIG. 12  shows a block diagram of yet another example of an implementation of an integrated low-loss directional bridge that utilizes a peak detector diode as a sensing element in accordance with the invention.  
         [0036]      FIG. 13  shows a block diagram of an example of an implementation of an integrated low-loss directional bridge that utilizes peak-to-peak detector diodes as a sensing element in accordance with the invention.  
         [0037]      FIG. 14  shows a block diagram of yet another example of an implementation of an integrated low-loss directional bridge that utilizes peak-to-peak detector diodes as a sensing element in accordance with the invention.  
         [0038]      FIG. 15  shows a block diagram of yet another example of an implementation of an integrated low-loss directional bridge that utilizes peak-to-peak detector diodes as a sensing element in accordance with the invention.  
         [0039]      FIG. 16  shows a block diagram of yet another example of an implementation of an integrated low-loss directional bridge that utilizes peak-to-peak detector diodes as a sensing element in accordance with the invention.  
         [0040]      FIG. 17  shows a block diagram of an example of an implementation of an integrated low-loss directional bridge utilizing a dual-directional bridge topology with paralleled low-pass directional bridge circuits with each bridge circuit sharing a common series inductor in accordance with the invention.  
         [0041]      FIG. 18  shows a block diagram of another example of an implementation of an integrated low-loss directional bridge utilizing a dual-directional bridge topology with cascaded high-pass and low-pass directional bridge circuits in accordance with the invention.  
         [0042]      FIG. 19  shows a block diagram of an example of an implementation of an integrated low-loss detector directional bridge utilizing a pair of quarter wavelength transmission line resonators in accordance with the invention.  
         [0043]      FIG. 20  shows a block diagram of another example of an implementation of an integrated low-loss directional bridge circuit in a low-pass configuration, having a coupling factor equal to −14 dB at a frequency of 1 GHz, in accordance with the invention.  
         [0044]      FIG. 21  shows a block diagram of an example of an implementation of the integrated low-loss directional bridge circuit shown in  FIG. 3 , having resistor elements and a coupling factor equal to −14 dB, in accordance with the invention.  
         [0045]      FIG. 22  shows a block diagram of a directional circuit having an ideal coupler with a coupling factor of −14 dB.  
         [0046]      FIG. 23  shows a block diagram of an example implementation of an integrated low-loss directional bridge having cascaded high-pass and low-pass bridge circuits in accordance with the invention.  
         [0047]      FIG. 24  shows a block diagram of an example of an implementation of an integrated low-loss directional bridge in a low-pass configuration having a diode peak detector without frequency compensation in accordance with the invention.  
         [0048]      FIG. 25  shows a block diagram of an example of an implementation of an integrated low-loss directional bridge in a high-pass configuration having a diode peak detector without frequency compensation in accordance with the invention.  
         [0049]      FIG. 26  shows a block diagram of an example of an implementation of an integrated low-loss directional bridge utilizing a directional bridge topology with cascaded high-pass and low-pass directional bridge circuits, with diode peak detectors and a detector output that is frequency compensated, in accordance with the invention.  
         [0050]      FIG. 27  shows a graphical representation of a plot of detector output in decibels (“dB”) versus frequency in gigahertz (“GHz”) for the examples of implementations of integrated low-loss directional bridge circuits shown in  FIGS. 24, 25 , and  26 .  
         [0051]      FIG. 28  shows a graphical representation of a plot of insertion gain in dBs versus frequency in GHz for the examples of implementations of integrated low-loss directional bridge circuits shown in  FIGS. 24, 25 , and  26 . 
     
    
     DETAILED DESCRIPTION  
       [0052]     In the following description of examples of embodiments, reference is made to the accompanying drawings that form a part hereof, and which show, by way of illustration, several specific embodiments in which the invention may be practiced. Other embodiments may be utilized and structural changes may be made without departing from the scope of the present invention.  
         [0053]     In general, the invention is an integrated low-loss directional bridge that includes a plurality of lumped two-terminal elements connected in a directional bridge circuit with a sensing element that is configured to respond to a voltage difference between two nodes of the directional bridge circuit. It is appreciated by those skilled in the art that numerous types of directional circuit topologies may be utilized. Examples of the sensing element may include a passive transformer, a passive diode, a power sensing device, a direct current coupled (“DC-coupled”) differential amplifier with a high common mode rejection ratio, a differential amplifier that is not DC coupled, a Gilbert Cell mixer with differential radio frequency (“RF”) input, other mixers or samplers with differential RF inputs, or an integrated transformer or balun. For an integrated low-loss directional bridge circuit that operates at DC, the sensing element operates at DC and is DC-coupled. If phase information is not desired, a power or voltage magnitude sensing device such as a detector diode may be utilized as the sensing element.  
         [0054]     In  FIG. 3 , a block diagram of an example of an implementation of an integrated low-loss directional bridge circuit  300  utilizing a directional circuit topology is shown in accordance with the invention. In general,  FIG. 3  is the integrated directional bridge circuit  200  of  FIG. 2  with the impedances Z 4    218  and Z 5    220  of  FIG. 2  being a very small impedance and a very large impedance, respectively. Thus Z 4    218  approximates a short circuit (where Z 4    218 =0 and there is no voltage between nodes  208  and  224 ), and Z 5    220  approximates an open circuit (where Z 5    220 =∞ and there is no current flow from node  224  to ground  228 ).  
         [0055]     The low-loss directional bridge circuit  300  may be in signal communication with a signal source  302  having a signal source impedance (“Z source ”)  304  and a load having a load impedance (“Z load ”)  306  via signal paths  308  and  310 , respectively. The low-loss directional bridge circuit  300  may include impedance elements Z 1    312 , Z 2    314 , and Z 3    316 , and sensing element  322 . In this example directional bridge circuit topology, the signal source impedance Z source    304  is in signal communication with impedance element Z 1    312 . The load impedance Z load    306  is in signal communication with both impedance elements Z 1    312  and Z 2    314 . The sensing element  322  is in signal communication with node  324  having a node voltage V 4 . Similarly, the sensing element  322  is also in signal communication with both Z 2    314  and Z 3    316  at node  326  having a node voltage V 3 . Z 3    316  is in signal communication with a common ground  328 .  
         [0056]     The impedance elements Z 1    312 , Z 2    314 , and Z 3    316  may be either reactive impedance elements, real impedance elements (i.e., resistive elements), or combinations of real and reactive elements based on the frequency range of operation of the low-loss directional bridge circuit  300 . The sensing element  322  (which may be a DC-coupled differential amplifier with a high common mode rejection ratio, or a Gilbert Cell mixer with differential RF input) senses the difference in voltage between node voltages V 3  and V 4  and produces a difference signal  330  of the voltage difference between node voltages V 3  and V 4  in both magnitude and phase, and characteristic impedance Z 0  of the directional bridge circuit  300  may be expressed as:  
               Z   0     =         Z   1     ⁡     (       Z   2     +     Z   3       )           Z   1     +     Z   2                 (   3   )             
 
 Z 0  is also the reference impedance of the incident and reflected waves  334  and  332 . 
 
         [0057]     As an example of operation, it is appreciated by those skilled in the art that the amplified difference signal  330  may be proportional to either the incident voltage signal (“V incident ”)  332  from the low-loss directional bridge circuit  300  to Z load    306  or the reflected voltage (“V reflected ”)  334  from Z load    306  to the low-loss directional bridge circuit  300 , relative to Z 0  and independent of impedances Z source    304 , Z load    306 , and sensing element  322 . It is also appreciated that a passive load Z load    306  produces V reflected    334  by reflecting V incident    332 . Additionally, it is appreciated that V reflected    334  may be generated by Z load , if Z load  is an active device.  
         [0058]     If the sensing element  322  is a differential amplifier such as an operational amplifier connected between the nodes  324  and  326 , the proportional factor (“k”) is equal to the amplifier gain of the differential amplifier multiplied by the coupling factor of the directional bridge. It is appreciated that based on the values of the impedance elements Z 1    312 , Z 2    314 , and Z 3    316 , the low-loss directional bridge circuit  300  may be configured to produce an amplified difference signal  330  that is proportional to either V incident    332  or V reflected    334 .  
         [0059]     In  FIG. 4 , a block diagram of an example of an implementation of an integrated low-loss directional bridge circuit  400  utilizing a directional circuit topology in a low-pass configuration that includes a series inductor  412 , a shunt resistor  414 , and a shunt capacitor  416 , is shown in accordance with the invention. The low-loss directional bridge circuit  400  may be in signal communication with a signal source  402  having a signal source impedance (“Z source ”)  404  and a load having a load impedance (“Z load ”)  406  via signal paths  408  and  410 , respectively.  
         [0060]     In this example, the sensing element  422  may be a differential amplifier and the low-loss directional bridge circuit  400  may be configured to produce the amplified difference signal  430  that is proportional to V incident    432 , the value of the amplified difference signal  430  may be approximately equal to kV incident , and the characteristic impedance Z 0  of the low-loss directional bridge circuit  400  may be expressed as:  
                 Z   0     =         jω   ⁢           ⁢     L   1     ⁢     R   2       +       L   1       C   3             jω   ⁢           ⁢     L   1       +     R   2           ,           (   4   )             
 
 where Z 0  is independent of Z source    404 , Z load    406 , and the sensing element  422 . It is appreciated by those skilled in the art that Z o  may differ from an ideal desired Z o  due to accidental (for example, process variations) or intentional changes in the impedance values of Z 1  through Z 3  and the low-loss directional bridge circuit  400  may still have satisfactory performance even if the difference signal  430  may not be exactly equal to kV incident . 
 
         [0061]     Similarly, in  FIG. 5 , a block diagram of an example of an implementation of a low-loss directional bridge circuit  500  utilizing a directional circuit topology in a high-pass configuration that includes a series capacitor  512 , a shunt resistor  514 , and a shunt inductor  516 , is shown in accordance with the invention. The low-loss directional bridge circuit  500  may be in signal communication with a signal source  502  having a signal source impedance (“Z source ”)  504  and a load having a load impedance (“Z load ”)  506  via signal paths  508  and  510 , respectively.  
         [0062]     In this example, Z 0  of the low-loss directional bridge circuit  500  may be expressed as:  
                 Z   0     =         R   2     +     jω   ⁢           ⁢     L   3           1   +     jω   ⁢           ⁢     C   1     ⁢     R   2             ,           (   5   )             
 
 where Z 0  is again independent of Z source    504 , Z load    506 , and the sensing element  522 . Again, it is appreciated that Z o  may differ from the ideal desired Z o  due to accidental (for example, process variation) or intentional changes in the impedance values of Z 1  through Z 3  and the low-loss directional bridge circuit may still have satisfactory performance even if the difference signal  530  may not be exactly equal to kV reflected . 
 
         [0063]     Similarly, in  FIG. 6 , a block diagram of an example of an implementation of a low-loss directional bridge circuit  600  utilizing a directional circuit topology in a bandpass configuration that includes a series resonator, a shunt resistor  614 , and a parallel resonator, is shown in accordance with the invention. The low-loss directional bridge circuit  600  may be in signal communication with a signal source  602  having a signal source impedance (“Z source ”)  604  and a load having a load impedance (“Z load ”)  606  via signal paths  608  and  610 , respectively.  
         [0064]     In this example, the series resonator includes capacitor C 1    612  and inductor L 1    618 , in series, and the parallel resonator includes capacitor C 3    616  and inductor L 3    620 , in parallel, and Z 0  of the low-loss directional bridge circuit  600  may be expressed as:  
               Z   0     =       j   ⁢           ⁢     (       ω   ⁢           ⁢     L   1       -     1     ω   ⁢           ⁢     C   1           )     ⁢     (       R   2     +     1     j   ⁢           ⁢     (       ω   ⁢           ⁢     C   3       -     1     ω   ⁢           ⁢     L   3           )           )           j   ⁢           ⁢     (       ω   ⁢           ⁢     L   1       -     1     ω   ⁢           ⁢     C   1           )       +     R   2                 (   6   )             
 
 where Z 0  is again independent of Z source    604 , Z load    606 , and the sensing element  622 . Again, it is appreciated that Z 0  may differ from the ideal desired Z 0  due to accidental (for example, process variation) or intentional changes in the impedance values of Z 1  through Z 3  and the low-loss directional bridge circuit may still have satisfactory performance even if the difference signal  630  may not be exactly equal to kV reflected . 
 
         [0065]     Equations (4), (5), and (6) imply that Z 0  is a function of frequency and that a different set of values for L, R, and C must be chosen for each frequency. However, for element values chosen for low insertion loss, Z 0  is approximately independent of frequency. Equation (7) below defines the element values for the low-insertion-loss case of the low-pass configuration of  FIG. 4 , equation (8) below defines the element values for the low-insertion-loss case of the high-pass configuration of  FIG. 5 , and equation (9) below defines the element values for the low-insertion-loss case of the bandpass configuration of  FIG. 6  when the frequency of operation is near resonance:  
               Z   0     ≈         L   1         R   2     ⁢     C   3         ⁢           ⁢   when   ⁢           ⁢   ω   ⁢           ⁢     L   1     ⁢     R   2     ⁢           ⁢   is   ⁢           ⁢   small   ⁢           ⁢   compared   ⁢           ⁢   to   ⁢           ⁢       L   1     /     C   3       ⁢           ⁢   and   ⁢           ⁢   ω   ⁢           ⁢     L   1     ⁢           ⁢   is   ⁢           ⁢   small   ⁢           ⁢   compared   ⁢           ⁢   to   ⁢           ⁢       R   2     .               (   7   )                 Z   0     ≈         L   3         R   2     ⁢     C   1         ⁢           ⁢   when   ⁢           ⁢   ω   ⁢           ⁢     L   3     ⁢           ⁢   is   ⁢           ⁢   large   ⁢           ⁢   compared   ⁢           ⁢   to   ⁢           ⁢     R   2     ⁢           ⁢   and   ⁢           ⁢   ω   ⁢           ⁢     C   1     ⁢     R   2     ⁢           ⁢   is   ⁢           ⁢   large   ⁢           ⁢   compared   ⁢           ⁢   to   ⁢           ⁢   1.             (   8   )                   Z   0     ≈       L   1         R   2     ⁢     C   3           ⁢           =           L   3         R   2     ⁢     C   1         ⁢           ⁢   where   ⁢           ⁢     ω   0   2       =       1       L   1     ⁢     C   1         =       1       L   3     ⁢     C   3         .                 (   9   )             
 
         [0066]     The properties of the directional bridge circuit that make the difference signal  330 ,  FIG. 3 , proportional to V incident    332  or V reflected    334 ,  FIG. 3 , are not affected by the impedance (“Z D ”) of the sensing element  322 ,  FIG. 3 , but the coupling factor and through-line insertion loss are dependent on Z D . The coupling factor is the ratio of the voltage difference between node voltages V 3  and V 4  to the voltage V incident  on the load. The through-line gain is the ratio of the voltage V incident  on the load to the voltage V incident  on the source, both voltages relative to Z 0 . Simple expressions for the coupling factor and through-line insertions loss can be derived where Z D  is large enough to be ignored. Examples of detector elements with high impedance are high input impedance differential amplifiers, diode peak detectors, and biased diode detectors with video resistances in the K ohm range.  
         [0067]     Equation 10 (coupling factor) and equation 11 (through-line gain) below are valid for the schematic shown in  FIG. 3  when Z D  is large enough to ignore in the calculations. Additionally, if Z 2  is made equal to Z 0 , the coupled signal is either +90 degrees or −90 degrees out of phase with V incident    332  or V reflected    334 ,  FIG. 3 .  
             Coupling_factor   =           Z   1     +     Z   2           Z   2     +     Z   3         +       Z   1       Z   0                 (   10   )                 Through_line   ⁢   _gain     =       1     1   +       Z   1       2   ⁢     Z   0         +         Z   1     +     Z   0         2   ⁢           ⁢     (       Z   2     +     Z   3       )             .             (   11   )             
 
         [0068]     The insertion loss of a directional bridge circuit may be decreased by adding matching components at the source port or the load port (or both). As long as these matching components are small, the operation of the directional bridge circuits will remain satisfactory for most applications while retaining the advantage of lower insertion loss. In  FIG. 7 , a block diagram of an example of an implementation of an integrated low-loss directional bridge circuit  700  utilizing a directional circuit topology in a low-pass configuration that further includes series matching capacitors C match    740  and  742 , is shown in accordance with the invention. The low-loss directional bridge circuit  700  may be in signal communication with a signal source  702  having a signal source impedance (“Z source ”)  704  and a load having a load impedance (“Z load ”)  706  via signal paths  708  and  710 , respectively.  
         [0069]      FIG. 8  shows a block diagram of an example of an implementation of an integrated low-loss directional bridge circuit  800  utilizing a directional coupling topology in a high-pass configuration that further includes series matching inductors L match    840  and  842 , in accordance with the invention. The low-loss directional bridge circuit  800  may be in signal communication with a signal source  802  having a signal source impedance (“Z source ”)  804  and a load having a load impedance (“Z load ”)  806  via signal paths  808  and  810 , respectively.  
         [0070]     In an integrated circuit (“IC”) process, inductors may be fabricated as spiral inductors made of metal and having a physical length. As such, there is always a parasitic series resistance associated with the inductors that may be compensated for by certain implementations of the invention.  FIG. 9  shows a block diagram of an example of an implementation of an integrated low-loss directional bridge circuit  900  utilizing a directional circuit topology in a low-pass configuration that includes a parasitic series resistor R parasitic    918 . The low-loss directional bridge circuit  900  may be in signal communication with a signal source  902  having a signal source impedance (“Z source ”)  904  and a load having a load impedance (“Z load ”)  906  via signal paths  908  and  910 , respectively.  
         [0071]     Z 0  of the low-loss directional coupling circuit  900  may be expressed as:  
               Z   0     =             R   parasitic     ⁢     R   2       +       R   parasitic       jω   ⁢           ⁢     L   1         +     jω   ⁢           ⁢     R   2     ⁢     L   1       +       L   1       C   3             R   parasitic     +     R   2     +     jω   ⁢           ⁢     L   1           .             (   12   )             
 
         [0072]     If R parasitic    918  is small compared to a), (and making the low insertion loss approximation shown in Equation 3), ωL 1 R 2  is small compared to ωL 1 /C 3 , and ωL 1  is small compared to R 2 , Z 0  of the low-loss directional coupling circuit  900  may be expressed as:  
               Z   0     =       R   parasitic     +         L   1         R   2     ⁢     C   3         .               (   13   )             
 
         [0073]     Characteristic impedance Z 0  and the element values in Equations (4), (5) and (6) are independent of frequency. This means that the coupled output signal (i.e., difference signal  330 ,  FIG. 3 ) from the low-loss directional bridge circuit is proportional to the wave incident on the load at all frequencies. The coupling factor, however, may vary with frequency. In the low-pass configuration of  FIG. 4 , the coupling factor increases as the frequency increases, and in the high-pass configuration of  FIG. 5 , the coupling factor decreases as the frequency increases. This coupling factor increase or decrease with an increase in frequency may be compensated for by designing the Sensing Element  322 ,  FIG. 3 , with a sloped frequency response.  
         [0074]     In  FIG. 10 , a block diagram of an example of an implementation of an integrated low-loss directional bridge circuit  1000  utilizing a directional circuit topology in a low-pass configuration that includes frequency compensation using a detector diode  1022 , is shown in accordance with the invention. The low-loss directional bridge circuit  1000  may be in signal communication with a signal source  1002  having a signal source impedance (“Z source ”)  1004  and a load having a load impedance (“Z load ”)  1006  via signal paths  1008  and  1010 , respectively. In  FIG. 10 , a low-pass filter is added to the Sensing Element of the low-loss directional bridge circuit  1000 , which in this case is a detector diode  1022 , yielding a flat overall coupling response over the desired frequency band.  
         [0075]     The low-pass filter may include resister R comp    1030  and capacitor C comp    1040 . Port  1042  may be a negative detector output. At the frequency of operation, C large    1036  may be large enough so that it has a low impedance and the AC voltage between node  1024  and signal path  1008  is negligible. R large    1038  may also be large enough so that there is negligible current flowing from node  1024  to port  1042  and the insertion loss from signal path  1008  to signal path  1010  is not increased. R large    1018  may also be large enough so that its impedance is high compared to the impedance of capacitor C 3    1016  at the frequency of operation.  
         [0076]     In the case of the bandpass configuration shown in  FIG. 6 , the coupling factor decreases as the frequency increases below resonance and increases as the frequency increases above resonance where resonance refers to the resonant frequency of the series resonator (C 1  and L 1 ) and the parallel resonator (C 3  and L 3 ). Near resonance, the slope of the coupling response with frequency approaches zero and the coupling response goes to zero at resonance (assuming lossless resonators). The bandpass directional bridge circuit requires operation below or above resonance unless the resistive components of the resonators at resonance satisfy the required impedance relationship of Equations (2) or (3).  
         [0077]     In general, the low-loss directional bridge circuits in the low-pass configurations shown in  FIGS. 4 and 7  include the series inductors L 1    412  and  712 , the shunt elements R 2    414  and  714  and C 3    416  and  716 , and the Sensing Elements  422  and  722 , respectively. The low-loss directional bridge circuits in a high-pass configuration shown in  FIGS. 5 and 8  include the series capacitor C 1    512  and  812 , the shunt elements R 2    514  and  814  and L 3    516  and  816 , and the Sensing Elements  522  and  822 , respectively. And the low-loss directional bridge circuit in a bandpass configuration shown in  FIG. 6  includes the series resonator, which includes capacitor C 1    612  and inductor L 1    618 , the shunt elements R 2    614  and the parallel resonator, which includes capacitor C 3    616  and inductor L 3    620 , and the Sensing Element  622 . The Sensing Elements may be implemented in various ways and each Sensing Element may also include associated circuitry for bias and output connections, temperature compensation, etc. As an example implementation, the Sensing Element may be a low-barrier square-law detector diode, a peak detector diode, a differential amplifier, a mixer or a sampler or other component that responds to the difference in voltage between nodes V 4  and V 3 .  
         [0078]      FIGS. 11 through 18  show block diagrams of low-loss directional bridge circuits with various Sensing Elements.  FIG. 11  shows a block diagram of an example of an implementation of a low-loss directional bridge circuit  1100  in a low-pass configuration where the Sensing Element is a peak detector diode  1122 . The low-loss directional bridge circuit  1100  may be in signal communication with a signal source  1102  having a signal source impedance (“Z source ”)  1104  and a load having a load impedance (“Z load ”)  1106  via signal paths  1108  and  1110 , respectively. C match and DC block    1138  and  1140  are matching capacitor elements and they may also function as DC blocks that are useful for preventing a DC voltage at signal paths  1108  or  1110 , respectively, from appearing at the detector output ports  1142  and  1144 . Port  1142  may be the positive detector output or the ground return for the negative detector output and port  1144  may be the negative detector output or the ground return for the positive detector output. At the frequency of operation, C large    1146  may be large enough so that it has a low impedance and the AC voltage between node  1124  and node  1148  is negligible. R large    1136  may also be large enough so that there is negligible current flowing from node  1124  to node  1142  and the insertion loss from signal path  1108  to signal path  1110  is not increased R large    1118  may also be large enough so that its impedance is high compared to the impedance of capacitor C 3    1116  at the frequency of operation.  
         [0079]      FIG. 12  shows a block diagram of another example of an implementation of a low-loss directional bridge circuit  1200  in a high-pass configuration where the Sensing Element is a peak detector diode  1222 . The low-loss directional bridge circuit  1200  may be in signal communication with a signal source  1202  having a signal source impedance (“Z source ”)  1204  and a load having a load impedance (“Z load ”)  1206  via signal paths  1208  and  1210 , respectively. C match and DC block    1238  and  1240  are matching capacitor elements and they may also function as DC blocks that are useful for preventing a DC voltage at signal paths  1208  or  1210 , respectively, from appearing at the detector output port  1242 . Port  1242  may be a positive detector output. R large    1236  may also be large enough so that there is negligible current flowing from node  1224  to port  1242  and the insertion loss from signal path  1208  to signal path  1210  is not increased.  
         [0080]     In  FIG. 13 , a block diagram of another example of an implementation of a low-loss directional bridge circuit  1300  in a low-pass configuration where the Sensing Element is a peak-to-peak detector having two detector diodes  1322  and  1336 . The low-loss directional bridge circuit  1300  may be in signal communication with a signal source  1302  having a signal source impedance (“Z source ”)  1304  and a load having a load impedance (“Z load ”)  1306  via signal paths  1308  and  1310 , respectively. C match and DC block    1338  and  1340  are matching capacitor elements and they may also function as DC blocks that are useful for preventing a DC voltage at signal paths  1308  or  1310 , respectively, from appearing at the detector output ports  1342  and  1344 . Port  1342  may be a negative detector output or a ground return for a positive detector output, and port  1344  may be a positive detector output or a ground return for a negative detector output. At the frequency of operation, C large    1350  may be large enough so that it has a low impedance and the AC voltage between node  1324  and node  1346  is negligible. At the frequency of operation, C large    1352  may be large enough so that it has a low impedance and the AC voltage between node  1348  and node  1324  is negligible. R large    1346  may be large enough so that there is negligible current flowing from node  1324  to port  1342  and the insertion loss from signal path  1308  to signal path  1310  is not increased. R large    1330  may also be large enough so that there is negligible current flowing from node  1348  to port  1344  and the insertion loss from signal path  1308  to signal path  1310  is not increased.  
         [0081]     In  FIG. 14 , a block diagram of yet another example of an implementation of a low-loss directional bridge circuit  1400  in a low-pass configuration where the Sensing Element is a peak-to-peak detector having two detector diodes  1422  and  1436 . The low-loss directional bridge circuit  1400  may be in signal communication with a signal source  1402  having a signal source impedance (“Z source ”)  1404  and a load having a load impedance (“Z load ”)  1406  via signal paths  1408  and  1410 , respectively. C match and DC block    1438  and  1440  are matching capacitor elements and they may also function as DC blocks that are useful for preventing a DC voltage at signal paths  1408  or  1410 , respectively, from appearing at the detector output ports  1442  and  1444 . Port  1442  may be a positive detector output or a ground return for a negative detector output, and port  1444  may be a negative detector output or a ground return for a positive detector output. At the frequency of operation, C large    1452  may be large enough so that it has a low impedance and the AC voltage between node  1424  and node  1454  is negligible. At the frequency of operation, C large    1446  may be large enough so that it has a low impedance and the AC voltage between node  1456  and node  1426  is negligible. R large    1448  may be large enough so that there is negligible current flowing from node  1426  to port  1442  and the insertion loss from signal path  1408  to signal path  1410  is not increased. R large    1450  may also be large enough so that there is negligible current flowing from node  1456  to port  1444  and the insertion loss from signal path  1408  to signal path  1410  is not increased.  
         [0082]     In  FIG. 15 , a block diagram of yet another example of an implementation of a low-loss directional bridge circuit  1500  in a low-pass configuration where the Sensing Element is a peak-to-peak detector having two detector diodes  1522  and  1536 . The low-loss directional bridge circuit  1500  may be in signal communication with a signal source  1502  having a signal source impedance (“Z source ”)  1504  and a load having a load impedance (“Z load ”)  1506  via signal paths  1508  and  1510 , respectively. C match and DC block    1538  and  1540  are matching capacitor elements and they may also function as DC blocks that are useful for preventing a DC voltage at signal paths  1508  or  1510  from appearing at the detector output ports  1542  and  1544 . Port  1542  may be a positive detector output or a ground return for a negative detector output, and port  1544  may be a negative detector output or a ground return for a positive detector output. At the frequency of operation, C large    1548  may be large enough so that it has a low impedance and the AC voltage between node  1556  and node  1558  is negligible. At the frequency of operation, C large    1546  may be large enough so that it has a low impedance and the AC voltage between V 4  node  1560  and node  1556  is negligible. R large    1550  may be large enough so that there is negligible current flowing from node  1558  to port  1542  and the insertion loss from signal path  1508  to signal path  1510  is not increased. R large    1530  may also be large enough so that there is negligible current flowing from node  1560  to port  1544  and the insertion loss from signal path  1508  to signal path  1510  is not increased.  
         [0083]     In  FIG. 16 , a block diagram of another example of an implementation of a low-loss directional bridge circuit  1600  in a low-pass configuration where the Sensing Element is a peak-to-peak detector having two detector diodes  1622  and  1636 . The low-loss directional bridge circuit  1600  may be in signal communication with a signal source  1602  having a signal source impedance (“Z source ”)  1604  and a load having a load impedance (“Z load ”)  1606  via signal paths  1608  and  1610 , respectively. C match and DC block    1638  and  1640  are matching capacitor elements and they may also function as DC blocks that are useful for preventing a DC voltage at signal paths  1608  or  1610 , respectively, from appearing at the detector output ports  1642  and  1644 . Port  1642  may be a negative detector output or a ground return for a positive detector output, and port  1644  may be a positive detector output or a ground return for a negative detector output. At the frequency of operation, C large    1648  may be large enough so that it has a low impedance and the AC voltage between node  1658  and node  1656  is negligible. At the frequency of operation, C large    1650  may be large enough so that it has a low impedance and the AC voltage between node  1660  and node  1656  is negligible. R large    1632  may be large enough so that there is negligible current flowing from node  1658  to port  1642  and the insertion loss from signal path  1608  to signal path  1610  is not increased. R large    1630  may also be large enough so that there is negligible current flowing from node  1660  to port  1644  and the insertion loss from signal path  1608  to signal path  1610  is not increased.  
         [0084]      FIG. 17  shows a block diagram of an example of an implementation of a low-loss directional bridge circuit  1700  utilizing a parallel dual-directional bridge topology with two differential amplifiers  1722  and  1736  in accordance with the invention. The low-loss directional bridge circuit  1700  may be in signal communication with a signal source  1702  having a signal source impedance (“Z source ”)  1704  and a load having a load impedance (“Z load ”)  1706  via signal paths  1708  and  1710 , respectively. Port  1742  may be an output port whose output is proportional to reflected voltage signal V reflected    1734 , and port  1744  may be an output port whose output is proportional to incident voltage signal V incident    1732 .  
         [0085]     In general, the integrated low-loss directional bridge  1700  is an implementation that is a lower-insertion loss alternative to an implementation formed by cascading two single-directional bridges having a low-pass configuration as described in  FIGS. 4 and 7 . This lower-insertion loss alternative is feasible if the differential input impedances of the differential amplifiers  1722  and  1736  are high and the impedance of the series combinations of resistor R 2    1714  and capacitor C 3    1716  and of resistor R 2    1738  and capacitor C 3    1740  is high compared to characteristic impedance Z 0 .  
         [0086]      FIG. 18  shows a block diagram of yet another example of an implementation of a low-loss directional bridge circuit  1800  utilizing a cascaded dual-directional bridge topology with two differential amplifiers  1822  and  1836  in accordance with the invention. The low-loss directional bridge circuit  1800  may be in signal communication with a signal source  1802  having a signal source impedance (“Z source ”)  1804  and a load having a load impedance (“Z load ”)  1806  via signal paths  1808  and  1810 , respectively. Port  1842  may be an output port whose output is proportional to reflected voltage signal V reflected    1834 , and port  1844  may be an output port whose output is proportional to incident voltage signal V incident    1832 .  
         [0087]     In general, the integrated low-loss directional bridge  1800  is an implementation that is similar to the implementation shown in  FIG. 17  with the exception that it is formed by cascading two single-directional bridges, with one having a low-pass configuration and the other a high-pass configuration. As in the implementation shown in  FIG. 17 , this implementation also requires that the differential input impedances of the differential amplifiers  1822  and  1836  are high and the impedance of the series combination of resistor R 2    1814  and capacitor C 3    1816  and of resistor R 4    1826  and inductor L 3    1830  are high compared to characteristic impedance Z 0 .  
         [0088]     In  FIG. 19 , a block diagram of an example of an implementation of a low-loss directional bridge circuit  1900  utilizing a directional circuit topology that includes a detector diode  1922 , and two quarter wavelength transmission line resonators  1912  and  1916 , is shown in accordance with the invention. The low-loss directional bridge circuit  1900  may be in signal communication with a signal source  1902  having a signal source impedance (“Z source ”)  1904  and a load having a load impedance (“Z load ”)  1906  via signal paths  1908  and  1910 , respectively. C match and DC block    1938  and  1940  are matching capacitor elements and they may also function as DC blocks that are useful for preventing a DC voltage at signal paths  1908  or  1910 , respectively, from appearing at the detector output port  1942 . Port  1942  may be a negative detector output. The low-loss directional bridge circuit  1900  may operate near resonance for low insertion loss, where Z 0 =(Z 01 )(Z 03 )/R 2 . Z 01  is the characteristic impedance of the series transmission line resonator  1912  and Z 03  is the characteristic impedance of the shunt transmission line resonator  1916 . R large    1930  may be large enough so that there is negligible current flowing from node  1932  to port  1942  and the insertion loss from signal path  1908  to signal path  1910  is not increased.  
         [0089]      FIGS. 20, 21 , and  22  show block diagrams of example implementations of low-loss directional bridge circuits  2000 ,  2100 , and  2200 , respectively, each with a coupling factor of −14 dB at 1 GHz and varying insertion gains. In  FIG. 20 , a block diagram of an example of an implementation of a low-loss directional bridge circuit  2000  in a low-pass configuration that includes a series inductor  2012 , a shunt resistor  2014 , and a shunt capacitor  2016 , is shown in accordance with the invention. In a specific implementation, inductor L 1    2012 =0.796 nH, resistor R 2    2014 =50 ohms, and capacitor C 3    2016 =0.318 pF. At a frequency of 1 GHz, the coupling factor is equal to −14 dB, with an insertion gain equal to −0.043 dB.  
         [0090]     In  FIG. 21 , a block diagram of an example of an implementation of the low-loss directional bridge circuit  2100  is shown in accordance with the invention. This low-loss directional bridge circuit  2100  is similar to that configuration shown in  FIG. 3  and is implemented entirely with resistors. In a specific implementation, resistor R 1    2112 =5 ohms, resistor R 2    2114 =50 ohms, and resistor R 3    2116 =500 ohms. At a broadband frequency, the coupling factor is equal to −14 dB, with an insertion gain equal to −0.82 dB.  
         [0091]     In  FIG. 22 , a block diagram of an example of an implementation of the ideal lossless directional coupler circuit  2200  with perfect match to characteristic impedance Z 0  is shown for purposes of comparison with low-loss directional bridge circuit in accordance with the invention. At a broadband frequency, the coupling factor is equal to −14 dB, with an insertion gain equal to −0.18 dB. For the ideal loss-less directional bridge circuit  2200 , the through-line gain is given by the following equation:  
                 Through_line   ⁢     _gain   Ideal_coupler       =     1     1   +     C   2           ,     where   ⁢           ⁢   C   ⁢           ⁢   is   ⁢           ⁢   the   ⁢           ⁢   coupling   ⁢     -     ⁢   factor   ⁢           ⁢   as   ⁢           ⁢   a   ⁢           ⁢   voltage   ⁢           ⁢     ratio   .               (   14   )             
 
         [0092]     As illustrated by  FIGS. 20, 21 , and  22 , a low-loss directional bridge circuit with reactive elements in accordance with the invention may have lower insertion loss than an ideal directional coupler circuit whenever the detector element has a high impedance. If, however, the impedance of the detector element were Z 0 , the ideal directional coupler circuit would have a lower insertion loss for the same coupling factor.  
         [0093]     As noted in the detailed description of  FIG. 10  above, the coupling factor of directional bridge circuits having a low-pass or a high-pass configuration may vary with frequency. In the low-pass configuration, the coupling factor increases as the frequency increases, and in the high-pass configuration, the coupling factor decreases as the frequency increases.  FIG. 10  shows a block diagram of an example of an implementation of an integrated low-loss directional bridge circuit  1000  that compensates for this frequency variation by utilizing a compensating filter in the detection circuitry. Another method for compensating for coupling frequency variation is to cascade a low-loss directional bridge in a low-pass configuration with a low-loss directional bridge in a high-pass configuration and then to sum the detector outputs of both circuits.  
         [0094]     In  FIG. 23 , a block diagram of an example of an implementation of a low-loss directional bridge circuit  2300  utilizing a dual-directional bridge topology formed by cascading two single-directional bridges, with one having a low-pass configuration and the other a high-pass configuration, is shown in accordance with the invention. The low-loss directional bridge circuit  2300  may be in signal communication with a signal source  2302  having a signal source impedance (“Z source ”)  2304  and a load having a load impedance (“Z load ”)  2306  via signal paths  2308  and  2310 , respectively. Z detector    2340  is a sensing element whose output is proportional to the incident voltage signal V incident    2332 , and Z detector    2342  is a sensing element whose output is also proportional to incident voltage signal V incident    2332 . The outputs of Z detector    2340  and Z detector    2342  are input to and summed in Detector Output Summing Circuit  2344 . Port  2346  is the output of Detector Output Summing Circuit  2344 .  
         [0095]     The method of summing outputs in a dual-directional bridge circuit may depend on the nature of the detection circuitry of the bridge circuits.  FIGS. 24, 25 , and  26  show block diagrams of various examples of implementations of low-loss directional bridge circuits without frequency compensation and with frequency compensation, with lumped elements given specific example values.  
         [0096]     In  FIG. 24 , a block diagram of an example of an implementation of an integrated low-loss directional bridge circuit  2400  utilizing a directional circuit topology in a low-pass configuration that includes a series inductor L 1    2412 , a shunt resistor R 2    2414 , and a shunt capacitor C 3    2416  and that utilizes a detector diode  2422 , is shown in accordance with the invention. Port  2442  is a positive detector output that is not frequency compensated.  
         [0097]     Illustrative values (for an operating frequency of 1 GHz) are as follows: inductor L 1    2412 =0.796 nH; resistor R 2    2414 =50 Ohms; and capacitor C 3    2416 =0.318 pF. Resistors R 9    2424  and R 11    2418  are set to 20K Ohms. Note that resistors R 9    2424  and R 11    2418  are the equivalents of resistors R large    1018  and  1038 ,  FIG. 10 . It is appreciated that resistors R 9    2424  and R 11    2418  may have values that are large enough so as to minimize the insertion loss and that the actual values chosen are not critical. Capacitor C 1    2426  is set to 10 pF. Note that capacitor C 1    2426  is the equivalent of capacitor C large    1036 ,  FIG. 10 . It is appreciated that capacitor C 1    2426  may have a low impedance at the operating frequency and that the actual value chosen is not critical. In general, for a fixed R 2 , the ratio of L 1 /C 3  may be kept constant; and L 1  and C 3  may be increased for a higher coupling factor and increased insertion loss.  
         [0098]     In  FIG. 25 , a block diagram of an example of an implementation of an integrated low-loss directional bridge circuit  2500  utilizing a directional circuit topology in a high-pass configuration that includes a series capacitor C 4    2512 , a shunt resistor R 2    2514 , and a shunt inductor L 1    2516  and that utilizes a detector diode  2522 , is shown in accordance with the invention. Port  2542  is a positive detector output that is not frequency compensated.  
         [0099]     Illustrative values (for an operating frequency of 1 GHz) are as follows: capacitor C 4    2512 =31.833 pF; resistor R 2    2514 =50 Ohms; and inductor L 1    2516 =79.555 nH. Resistor R 9    2528  is set to 10K Ohms. Note that resistor R 9    2528  is the equivalent of resistors R large    1236 ,  FIG. 12 . It is appreciated that resistor R 9    2524  may have values that are large enough so as to minimize the insertion loss and that the actual value chosen is not critical. Capacitor C 1    2518  is set to 10 pF. Note that capacitor C 1    2518  is the equivalent of capacitor C large    1136 ,  FIG. 11 . It is appreciated that capacitor C 1    2518  may have a low impedance at the operating frequency and that the actual value chosen is not critical. In general, for a fixed R 2 , the ratio of L 1 /C 3  may be kept constant; and L1 and C3 may be decreased for a higher coupling factor and increased insertion loss.  
         [0100]     In  FIG. 26 , a block diagram of an example of an implementation of an integrated low-loss directional bridge circuit  2600  utilizing a directional circuit topology formed by cascading two single-directional bridges, with one having a low-pass configuration and the other a high-pass configuration, is shown in accordance with the invention. Low-loss directional bridge circuit  2600  includes a series inductor L 1    2612 , a shunt resistor R 2    2614 , a shunt capacitor C 3    2616 , a series capacitor C 4    2632 , a shunt resistor R 12    2634 , a shunt inductor L 2    2636 , detector diodes  2622  and  2624 , resistors R 9    2622  and R 13    2618 , and capacitors C 1    2642  and C 5    2644 . Port  2650  is the positive detector output that is frequency compensated.  
         [0101]     Illustrative values (for an operating frequency of 1 GHz) are as follows: inductor L 1    2612 =0.796 nH; resistor R 2    2614 =50 Ohms; capacitor C 3    2616 =0.318 pF; capacitor C 4    2632 =31.822 pF; resistor R 12    2634 =50 Ohms; and inductor L 2    2636 =79.555 nH. Resistors R 9    2622  and R 13    2618  are set to 20K Ohms. Note that resistors R 9    2622  and R 13    2618  are the equivalents of resistors R large    1018  and  1038 ,  FIG. 10 . It is appreciated that resistors R 9    2622  and R 13    2618  may have values that are large enough so as to minimize the insertion loss and that the actual values chosen are not critical. Capacitors C 1    2642  and C 5    2644  are set to 10 pF. Note that capacitors C 1    2642  and C 5    2644  are the equivalent of capacitor C large    1036 ,  FIG. 10 . It is appreciated that capacitors C 1    2642  and C 5    2644  may have a low impedance at the operating frequency and that the actual value chosen is not critical.  
         [0102]      FIG. 27  shows a graphical representation of a plot of detector output in decibels (“dBV”) versus frequency in gigahertz (“GHz”) for the examples of implementations of integrated low-loss directional bridge circuits shown in  FIGS. 24, 25 , and  26 . Line  2702  shows the plot for the low-loss directional bridge circuit  2400  having a low-pass configuration shown in  FIG. 24 ; line  2704  shows the plot for the low-loss directional bridge circuit  2500  having a high-pass configuration shown in  FIG. 25 ; and Line  2706  shows the plot for the low-loss directional bridge circuit  2600  having a cascaded low-pass and high-pass bridge configuration shown in  FIG. 26 .  
         [0103]     In general, the graphical representation of  FIG. 27  shows that as the frequency increases in a low-pass low-loss directional bridge circuit, the coupling factor increases (plot  2702 ), and that as the frequency increases in a high-pass low-loss directional bridge circuit, the coupling factor decreases (plot  2704 ). By utilizing a directional circuit topology formed by cascading a high-pass directional bridge and a low-pass directional bridge, as shown in  FIG. 26 , a bridge circuit is produced that has a flatter frequency response and a higher coupling factor at the operating frequency, as shown by plot  2706 .  
         [0104]      FIG. 28  shows a graphical representation of a plot of insertion gain in dB versus frequency in GHz for the examples of implementations of integrated low-loss directional bridge circuits shown in  FIGS. 24, 25 , and  26 . Line  2802  shows the plot for the low-loss directional bridge circuit  2400  having a low-pass configuration shown in  FIG. 24 ; line  2804  shows the plot for the low-loss directional bridge circuit  2500  having a high-pass configuration shown in  FIG. 25 ; and Line  2806  shows the plot for the low-loss directional bridge circuit  2600  consisting of cascaded low-pass and high-pass low-loss directional bridges shown in  FIG. 26 .  
         [0105]     In general, the graphical representation of  FIG. 28  shows that as the frequency increases in a low-pass low-loss directional bridge circuit, the insertion gain decreases (plot  2802 ), and that as the frequency increases in a high-pass low-loss directional bridge circuit, the insertion gain increases (plot  2804 ). Plot  2806  shows that a cascaded low-pass high-pass directional bridge circuit, as shown in  FIG. 26 , has a lower insertion gain throughout its frequency range  
         [0106]     While the foregoing description refers to the use of an integrated directional low-loss bridge, the subject matter is not limited to such a system. Any directional bridge system that could benefit from the functionality provided by the components described above may be implemented in the example implementation of Low-Loss Directional Bridge 300.  
         [0107]     Moreover, it will be understood that the foregoing description of numerous implementations has been presented for purposes of illustration and description. It is not exhaustive and does not limit the claimed inventions to the precise forms disclosed. Modifications and variations are possible in light of the above description or may be acquired from practicing the invention. The claims and their equivalents define the scope of the invention.