Abstract:
In an embodiment, a termination for a transmission line (or high frequency circuit) includes a matching circuit which provides a matching impedance for the transmission line and an electrical connection between the two, e.g., a bond wire. The electrical connection has a reactance matrix, which, when combined with the impedance provided by the matching circuit, provides a resultant termination resistance.

Description:
BACKGROUND 
   This invention relates generally to microwave and millimeter wave (mm-wave) radio frequency (RF) circuits, and more particularly to terminations for transmission line and one-sided matching to include wire bond inductances. 
   It is well known that an impedance change can cause signal reflection in high speed circuits. The reflection coefficient is given by: 
             Γ   =         Z   L     -     Z   o           Z   L     +     Z   o                 (     eq   .           ⁢   1     )             
 
where Z L  is the load impedance and Z o  is the transmission line characteristic impedance. When transmission lines end in an open circuit, Z L  is infinity. As a result Γ is one and the signal is entirely reflected back. It is therefore important to provide a match termination to reduce reflection and signal bounce in many high speed circuits such as hybrid couplers, T/R modules, circulators, power combiners, absorptive filters, doublers, mixers couplers and so on. In addition, a typical high frequency switch-matrix used for optical signal routing has N by N lines crossing each other and going to the edge of the chip. Each of the line ends need termination. Thus a total of N 2  terminations are required. Since the switch-matrixes are made on an expensive substrate such as Indium Phosphide (InP) or Gallium Arsenide (GaAs) to allow high frequency signal processing, it may be desirable to terminate these transmission lines in their characteristic impedance outside the integrate circuit (IC). Often the terminations need to absorb 1-5 W of power and have broadband width (e.g., DC-to-40 GHz).
 
   Since high power terminations require large chip area and are built on thermally conductive substrates such as Aluminum Nitride (AlN) and Beryllium Oxide (BeO), they are often included outside the expensive InP or GaAs chip. Moreover, a single bond-wire is often desirable as it is compatible for large-scale manufacturing. The bond wire is electrically represented by an equivalent circuit that usually comprises of a reactance matrix comprising of shunt capacitance followed by a series inductance and another shunt capacitance. The reactance matrix is dominated by the series inductance. 
   SUMMARY 
   In an embodiment, a termination for a transmission line (or high frequency circuit) includes a matching circuit which provides a matching impedance for the transmission line and an electrical connection between the two, e.g., a bond wire. The electrical connection has a reactance matrix, which, when combined with the impedance provided by the matching circuit, provides a resultant termination resistance. 
   The matching circuit may include grounding means, passive elements, and a thin film resistor (which may be monolithic or multi-sectioned). The dimensions and geometry of the thin film resistor may be selected to provide a negative inductance which matches the bond wire inductance. 
   The termination is on a different substrate than the transmission line. The material used for the termination substrate may be less expensive than that used for the transmission line. Substantially all matching is provided on the termination. 
   The termination may provide high power handling (&gt;1 W) and a high frequency bandwidth (e.g., DC-to-40 GHz). 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a perspective view of a transmission line connected to a termination by a bond wire. 
       FIG. 2  is a schematic representation of a negative impedance lumped element circuit. 
       FIG. 3  is a plan view of a termination according to an embodiment. 
       FIG. 4  is a graph showing impedance versus length for a thin film resistor in the termination. 
       FIG. 5  is a schematic representation of current flow in the resistor. 
       FIG. 6  is a Smith chart showing the negative inductance produced by an 800 μm long termination over a frequency sweep of 2-42 GHz frequency sweep. 
       FIG. 7  is a Smith chart showing the match of the bond-wire and the termination. 
       FIG. 8  is a plan view of a termination according to an embodiment. 
       FIG. 9  is a graph showing return loss for the termination. 
       FIG. 10  is a plan view of a termination according to an embodiment. 
       FIG. 11  is a graph showing return loss for the termination. 
       FIG. 12  is a perspective view of a transmission line connected to a termination by a bond wire. 
       FIG. 13  is a Smith chart showing the match of the bond-wire and the termination. 
       FIG. 14  is a graph showing return loss for the termination. 
       FIGS. 15A-15C  are sectional views of the termination of FIG.  1 . 
       FIG. 16  Smith Chart representation of the two-section thin film resistor matching network. 
       FIG. 17  is a graph showing return loss for the termination. 
   

   DETAILED DESCRIPTION 
     FIG. 1  shows a load termination  105  connected to a transmission line  110  by a bond wire  115 . The termination includes a thin film resistor that provides impedance matching for the transmission line. The thin film resistor may compensate for the inductance of the bond wire by creating an impedance that looks like a negative inductance. The thin film resistor may enable the termination to provide high power handling (&gt;1 W) and high frequency bandwidth (e.g., DC-to-40 GHz). 
   The thin film resistor may be provided on a planar substrate, e.g., a glass chip. The dimensions and configuration of the thin film resistor(s) may be selected to produce a negative inductance that substantially matches the inductance of the bond wire, thereby compensating for the bond wire inductance. All matching components may be provided on the chip resistor. 
   At a single frequency, a negative inductor may be indistinguishable from a capacitor. However, the impedance of the negative inductor increases with increasing frequency. The following analysis derives an approximate equation confirming the existence of negative inductance. For lossy circuit line we have:
 
 Z   in   =Z   o  tan  h (γ d ) (For lossy short circuit line)  (eq. 2)
 
Where 
               Z   o     =         R   +     j   ⁢           ⁢   ω   ⁢           ⁢   L         j   ⁢           ⁢   ω   ⁢           ⁢   C                 (     eq   .           ⁢   3     )             
 
and
 
γ=√{square root over (( R+jωL ) jωC )}  (eq. 4)
 
If □d is much smaller than 1 then since: 
               tanh   ⁡     (   x   )       =     1   -       x   3     3     +   …             (     eq   .           ⁢   5     )             
         it follows that: 
               Z     i   ⁢           ⁢   n       =       Z   o     (       γ   ⁢           ⁢   d     -       γ   ⁢           ⁢     d   3       3     +   …     ⁢           )             (       eq   .           ⁢   6     ⁢   a     )             or                                 ⁢     ≈           R   +     j   ⁢           ⁢   ω   ⁢           ⁢   L         j   ⁢           ⁢   ω   ⁢           ⁢   C         ⁢     (         (         (     R   +     j   ⁢           ⁢   ω   ⁢           ⁢   L       )     ⁢   j   ⁢           ⁢   ω   ⁢           ⁢   C       )     ⁢   d     -           (         (     R   +     j   ⁢           ⁢   ω   ⁢           ⁢   L       )     ⁢   j   ⁢           ⁢   ω   ⁢           ⁢   C       )     3     ⁢     d   3       3       )                 (       eq   .           ⁢   6     ⁢   b     )                 ≈     Rd   +     j   ⁢           ⁢   ω   ⁢           ⁢   Ld     -     j   ⁢           ⁢   ω   ⁢           ⁢   C   ⁢           ⁢         R   2     ⁢     d   3       3       +     2   ⁢   R   ⁢           ⁢         ω   2     ⁢     LCd   3       3       +     j   ⁢           ⁢     ω   3     ⁢           ⁢         L   2     ⁢     Cd   3       3           ⁢                   (       eq   .           ⁢   6     ⁢   c     )             
 
For the imaginary part to be negative we require: 
               j   ⁢           ⁢   ω   ⁢           ⁢   C   ⁢           ⁢         R   2     ⁢     d   3       3       &gt;       j   ⁢           ⁢   ω   ⁢           ⁢   L   ⁢           ⁢   d     +     j   ⁢           ⁢     ω   3     ⁢         L   2     ⁢     Cd   3       3                 (     eq   .           ⁢   7     )             or                             C   L     ⁢         R   2     ⁢     d   2       3       &gt;     1   +       ω   2     ⁢       LCd   2     3                 (     eq   .           ⁢   8     )             
 
If the length of the resistor is small then the second term on right is small, and 
                   C     3   ⁢   L         ⁢   Rd     &gt;   1           (       eq   .           ⁢   9     ⁢   a     )             or                         Rd   &gt;         3   ⁢   L     C               (       eq   .           ⁢   9     ⁢   b     )             
       

   A description of the equation analysis begins with the input impedance of eq. 2. The impedance Z in  depends on the characteristic impedance of the transmission line Z o  from eq. 3 and the propagation constant γ from eq. 4. Zo and γ are integrated in eq. 2, by using hyperbolic tangent approximation of eq. 5. The result is shown in eq. 6 going through steps from 6a to 6c. Eq. 7 sets a condition for which the imaginary part of eq. 6c becomes negative. Becoming negative, it creates a negative inductance. Condition from eq. 7 is simplified in eq. 8. Considering the small length of the resistor, eq. 9a evolved from eq. 8. The resistance and its length are related to the inductance and capacitance of the thin film resistor by eq. 9b. 
     FIG. 2  shows a schematic representing a negative impedance lumped element circuit  200 . This figure consists of three elements. Capacitance to ground  205  is related to the width and length of the thin film resistor and to the substrate thickness of the termination. The inductance  210  is the negative inductance. The resistance  215  is the real part of the impedance of the thin film resistor. 
     FIG. 3  shows a termination according to an implementation. The termination includes a 200 μm wide thin film resistor  305  on an 8 mil glass substrate  310 . By varying the length and width of the thin film resistor  305 , the negative inductance may be balanced to that of the bond wire  115 .  FIG. 4  is a graph showing impedance versus length for the thin film resistor. Resistance  405  and reactance  410  are plotted at 40 GHz. The resistance length of 800 μm at the minimum reactance  415  value produces 150 Ohms of resistance. The reactance includes a transmission line to resistor film discontinuity due to current redistribution, referred to as contact inductance. The transition  315  between transmission line  320  and the thin film resistor  305  is presented in FIG.  5 . Current flows on the transmission line edges, as expected. The same current flows uniformly throughout the film resistor. In the transition region the current density is distributed in the manner of uniform tendency  505 . 
   Discontinuity of the transition is related to additional inductance. This inductance may be suppressed by a matching technique according to an implementation.  FIG. 6  is a Smith chart showing the negative inductance produced by an 800 μm long termination over a frequency sweep of 2-42 GHz frequency sweep  600 . A Smith chart is a graphical plot of normalized resistance and reactance functions in the reflection-coefficient plane, which may be used for impedance matching. The chart is a chart of r-circles  601  and x-circles  602  in the Γ r -Γ i  plane for |Γ|≦1. The intersection of an r-circle and an x-circle defines a point that represents a normalized load impedance Z L =r+jx.  FIG. 7  is a Smith chart showing the match  700  of the bond-wire and the termination. The bond wire has 0.3 nH of a maximum allowable inductance and is connected to a 150 Ohm impedance. 
     FIG. 8  shows an exemplary termination  800  according to an alternative implementation. The termination includes a parallel combination of 200 μm wide thin film resistors  805 . Three 150 Ohm resistors  300  in parallel may be used to match a 0.07 nH maximum allowable inductance. The return loss  900  for this termination is shown in FIG.  9 . The width of the terminating resistor may be expanded to 400 μm on the 8 mil glass substrate to produce an impedance of 100 Ohms. In this case, a thin resistor termination length of 950 μm may be used to match a bond wire inductance of 0.23 nH. 
     FIG. 10  shows a termination  1000  including two 100 Ohm thin film resistors  1005  in parallel. This parallel combination of 400 μm long resistor film terminations may be laid on an 8 mil glass substrate. This termination may be used to cancel a 0.1 nH bond wire inductance. The return loss  1100  for the termination shown in  FIG. 10  is shown on FIG.  11 . 
   The width of the termination may be expanded to 800 μm. The impedance of the thin film resistor is 50 Ohms when the termination length is 1050 μm. This length of thin film resistor may be used to match a maximum allowable bond wire inductance of 0.15 nH. 
   The return loss may become worse when the width of the termination resistor is expanded. However, the lower impedance values and higher resistor widths directly correspond to power handling levels. The tradeoff may be considered when designing a termination for a transmission line. Depending on the application, an ‘on termination matching’ technique may be used for 50, 75 and 150 Ohm transmission line terminations. 
   Clarification of the concept of negative inductance provided means to consider structures in which a bondwire is used to connect the transmission line to a multi-section thin film resistor. In the case of a short bond wire, the termination may be connected to the transmission line and matching on the line may be used to account for the transition. Methods of short and open stubs may be applied for matching purposes. Long bond wire termination across the gap may also be used. 
   A single-section thin film resistor  1205  with pad  1210 , such as that shown in  FIG. 12 , may be used to reduce contact inductance and further improve the matching. The matching  1300  of the bond wire inductance is shown on the Smith chart of FIG.  13  and its respective return loss  1400  in FIG.  14 . 
   Referring to  FIG. 1 , a multi-section matching structure according to an implementation includes a two-section thin film resistor termination  150  and  155 . The termination is laid on 125 mm thin film glass substrate  180 . Via holes  165  connect the first impedance section  150  to ground from the one side. A strip transition impedance  170  connects the two impedance sections. The second impedance section  155  is connected with the bond wire  115  to the external transmission line  111 . 
   The resistance of the thin film resistance is 35-Ohm-per square and expected power handling greater then 1-2 Watts. A cross sectional view of the structure from  FIG. 1  is shown in  FIG. 15A , and the left and right cross sectional views are shown in  FIGS. 15B and 15C . As shown in  FIG. 1 , the bond wire  115  connects the transmission line on an Indium Phosphate substrate  175  and the termination on the glass substrate  180 . Silicon  185  may be used on the back of the glass substrate  180 . 
   The Smith Chart representation of the two-section thin film resistor matching network is shown in FIG.  16 . The length of the first impedance section  150  is adjusted to about 25 Ohms ( 1600 ). Certain negative inductance  1601  is observed due to the length as well as width of the thin film resistor and thickness of the substrate  180 . The second impedance section  155  is set to about 25 Ohms to give a total of 50 Ohms ( 1602 ) by adjusting its parameters. Negative inductance  1603  due to the second impedance section is added. The total negative inductance, due to each section, has the same value as bond wire inductance, and the two inductances cancel as a result of matching. Note that the term “negative inductance” is used instead of “capacitive reactance” in reference to canceling the bond wire inductance. 
   By using negative inductance high port isolation is achieved. As shown in  FIG. 17 , the return loss of this structure is less than 20 dB in up to 40 GHz frequency range. 
   A number of embodiments have been described. Nevertheless, it will be understood that various modifications may be made without departing from the spirit and scope of the invention. Accordingly, other embodiments are within the scope of the following claims.