Abstract:
The present invention describes the method and system of applying filter synthesis technique to distributed amplifier design. The method for synthesizing a distributed amplifier comprises the steps of determining an appropriate filter design characteristic, computing inductor and capacitor values, converting the equivalent values into a distributed amplifier with response characteristics that mirror that of the chosen filter. Applying filter synthesis techniques to distributed amplifier design results in predictable amplifier response characteristics. Filter synthesis techniques are used to design filters with controllable characteristics such as gain, cut-off frequency, and roll-off slope. Depending on the desired filter characteristics, appropriate inductor and capacitor sizes can be determined. Transferring these chosen inductors and capacitors sizes to the distributed amplifier results in amplitude and phase responses that behave like a preferred embodiment or prototype filter.

Description:
FIELD OF THE INVENTION 
     This invention relates to distributed amplifier circuit design, more particularly to the application of filter synthesis techniques for controlling distributed amplifier characteristics. 
     BACKGROUND OF THE INVENTION 
     Distributed amplifiers are common circuits found in numerous applications such as telecommunications, sensing, and instrumentation. A principal feature of distributed amplifiers is that it provides broad frequency amplification with nearly uniform gain and delay response. Synthesis of these amplifiers has been primarily based on synthetic transmission line construction, i.e. uniform unit cells. This structure poses several disadvantages, the two most significant being large gain ripple and large group delay variation as the signal frequency approaches the band-edge. The effect of these performance limitations is significantly distorted signals, e.g. pulse waveforms. Reducing or eliminating gain and/or delay variations maintain the integrity of the signal as it passes through the distributed amplifier. To date, the primary approach to improving the response of distributed amplifiers has been to reduce the size of the uniform sections. This is an incomplete approach that also degrades circuit performance. Numerous other improvements have also been documented, but none address the problems of gain and delay variation. As the speed of digital signal transmission increases and higher frequencies are used, the detrimental effects of gain and delay variations increase as well. 
     Accordingly, there is a need for a distributed amplifier that produces a more uniform gain and delay over a wide bandwidth. 
     SUMMARY OF THE INVENTION 
     The present invention describes the method and system of applying filter synthesis techniques to distributed amplifier design. The method for synthesizing a distributed amplifier comprises the steps of determining an appropriate filter design characteristic, computing inductor and capacitor values, converting the equivalent values into a distributed amplifier with response characteristics that mirror that of the chosen filter. 
     Applying filter synthesis techniques to distributed amplifier design results in predictable amplifier response characteristics. Filter synthesis techniques are used to design filters with controllable characteristics such as gain, cut-off frequency, and roll-off slope. Depending on the desired filter characteristics, appropriate inductor and capacitor sizes can be determined. Transferring these chosen inductors and capacitors sizes to the distributed amplifier results in amplitude and phase responses that behave like the preferred embodiment or prototype filter. Advantageously, this method of utilizing filter-based L-C (Inductor-Capacitor) sizes provides improved performance of the distributed amplifier; e.g. minimal amplitude variation, minimal delay variation, controlled roll-off characteristics. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a prior art circuit diagram that illustrates a distributed amplifier design with an L-C ladder network. 
     FIG. 2 is a circuit diagram that illustrates an equivalent model of a transistor in accordance with the present invention. 
     FIG. 3A illustrates a symbol for a transmission line in accordance with the present invention. 
     FIG. 3B is a circuit diagram that illustrates the T-model approximation of a transmission line in accordance with the present invention. 
     FIG. 3C is a circuit diagram that illustrates the Pi-model approximation of a transmission line in accordance with the present invention. 
     FIG. 3D is a cascade of a plurality of transmission lines approximated by the Pi-model. 
     FIG. 4 is a circuit diagram that illustrates a preferred embodiment of a L-C filter in accordance with the present invention. 
     FIG. 4B is a circuit that illustrates a distributed amplifier design with transmission line components replaced with Pi-model approximations and transistors replaced with equivalent models based on the L-C filter in FIG.  4 A. 
     FIG. 5 is a flow diagram that illustrates the steps of constructing a distributed amplifier based on filter-synthesis techniques in accordance with the present invention. 
     FIG. 6 is a circuit diagram that illustrates one implementation of a distributed amplifier in a single-ended transmission mode. 
     FIG. 7 is a circuit diagram that illustrates another implementation of a distributed amplifier in a differential transmission mode. 
    
    
     DETAILED DESCRIPTION 
     FIG. 1 is a circuit diagram that depicts the topology of a distributed amplifier with an L-C ladder network. The figure comprises a series of transistors, in this embodiment depicted as field-effect transistors (FETs)  105   a,    105   b,    105   c,    105   d,  and  105   e,  separated by transmission lines  110   a,    110   b,    115   a,    115   b,    120   a,    120   b,    125   a,  and  125   b.  A transistor&#39;s output capacitance is usually smaller than its input capacitance, so capacitors  130   a - 130   e  are utilized to match capacitances on the output line (the transmission line comprising transmission lines  110   a,    115   a,    120   a - 125   a ) with the input line (the transmission line comprising lines  110   b,    115   b,    120   b - 125   b ). 
     Distributed amplifier  100  is shown with an indeterminate number of stages. Generally, gain increases for each stage that is added, but is limited by attenuation from the transmission lines  110   a,    110   b,    115   a,    115   b,    120   a,    120   b,    125   a,  and  125   b,  and transistors  105   a,    105   b,    105   c,    105   d,  and  05   e.  Beyond an optimum number of stages, the gain achieved from an additional stage is superseded by the increased attenuation from the added transmission lines and transistors. 
     The parasitic capacitances of the transistors  105   a - 105   e  within distributed amplifier  100  are compensated to have minimal effect. Transistors contain spurious reactive elements that restrict its performance, but a network of inductors and capacitors behaving as an artificial transmission line neutralize the parasitic elements within the circuit. This allows distributed amplifiers to have higher bandwidth capabilities than typical amplifiers. 
     FIG. 2 is a circuit diagram that illustrates the ideal equivalent of a transistor. This simplified model that describes the behavior of the transistor, much like the T-model or Pi-model apply to transmission lines. Node  220  corresponds to the gate, node  225  corresponds to the drain, and node  230  corresponds to the source. Current source  210  provides a current that is dependant on the voltage applied between node  220  and node  230 . The ratio of the voltage between node  220  and node  230  to the current output of the current source  210  is determined by the transconductance of transistor  200 , which is dictated by the size of the transistor. Capacitors  205  and  215  represent the internal capacitances of the transistor, as previously referred to as parasitic elements that limit the performance of circuits utilizing this device. The value of these capacitors also depends upon transistor size. These internal capacitances are to be appropriately matched with the transmission lines to behave as the preferred embodiment of L-C filter. 
     The design of the distributed amplifier is not restricted to field-effect transistors as shown in the current embodiment. The same concepts can be applied to other transistor devices, e.g. bipolar junction transistors. 
     FIG. 3A illustrates a symbol for a transmission line such as  110   a.  Node  305   a  represents the input node, and node  310   a  represents the output node.  300   a  is placed between stages of distributed amplifier  100 , and behaves with characteristics that can be modeled with reactive elements, i.e. inductors and capacitors. These reactive elements are chosen to appropriately balance the internal capacitances  205  and  215  of transistor  200 . Using transmission line  300 &#39;s parameters of transmission line length (Lline) impedance (Zline) and velocity (Vline), an equivalent circuit of inductors and capacitors can be constructed. 
     FIG. 3B is a circuit diagram that illustrates the T-model approximation of a transmission line. This approximation comprises inductors  315   b  and  320   b,  with capacitor  325   b  coupled to a voltage reference. Node  305   b  represents the input node, and node  310   b  represents the output node. 
     For the purpose of this specification, the convention L(A) will refer to the inductance of device A, and the convention C(B) will refer to the capacitance of device B. For example, C( 325   b ) refers to the capacitance of capacitor  325   b.    
     The conversion equations for L( 315   b ) and L( 320   b ) and C( 325   b ) are: 
     
       
           L ( 315   b )= L ( 320   b )=(( L line* Z line)/ Vline )/2 
       
     
     
       
           C ( 325   b )=( L line/( Z line* V line)) 
       
     
     FIG. 3C is a circuit diagram that illustrates the Pi-model approximation of a transmission line. This approximation comprises inductor  315   c  with capacitors  320   c  and  325   c  coupled to a voltage reference. Node  305   c  represents the input node, and node  310   c  represents the output node. The values of the inductance and capacitances are as follows: 
     
       
           L ( 315   c )=(( L line* Z line)/ V line) 
       
     
       C ( 320   c )= C ( 325   c )=( L line/( Z line* V line))/2 
     FIG. 3D is a cascade of a plurality of transmission lines approximated by the Pi-model. For the purpose of building a distributed amplifier, the number of transmission lines is one fewer than the number of desired stages. 
     FIG. 4B is a circuit that illustrates a distributed amplifier design  401  with transmission line components replaced with Pi-model approximations and transistors replaced with ideal equivalents, which is drawn from a preferred embodiment of a L-C filter  400  in accordance with the present invention. From the resulting circuit diagram the interactions between reactive elements are clear. Consistent with circuit theory, the following relationships hold: 
     
       
           C   1 = C ( 305   d ) 
       
     
     
       
           C   2 = C ( 310   d )+ C ( 315   d ) 
       
     
     
       
           L   1 = L ( 345   d ) 
       
     
     
       
           C   3 = C ( 320   d )+ C ( 325   d ) 
       
     
     
       
           L   2 = L ( 350   d ) 
       
     
     
       
           C   4 = C ( 330   d )+ C ( 335   d ) 
       
     
     
       
           L   3 = L ( 355   d ) 
       
     
     These variables represent the inductor and capacitor values that are needed to synthesize the filter with our desired response. Constructing the distributed amplifier with these values requires matching these values with the following equations: 
     
       
           C ( 410   a )= C ( 410   c )= C ( 410   d )= C ( 410   f )  Eq. 1 
       
     
     
       
           L   1 = L ( 410   e )= L ( 410   b )  Eq.2 
       
     
     
       
           C   1 = C ( 415   a )+ C ( 410   d )= C ( 415   c )+ C ( 405   a )+ C ( 410   a )  Eq. 3 
       
     
       C   2 = C ( 425   a )+ C ( 410   f )+ C ( 420   d )= C ( 425   c )+ C ( 405   b )+ C ( 410   c )+ C ( 420   a )  Eq. 4 
     
       
           L   2 = L ( 420   b )= L ( 420   e )  Eq. 5 
       
     
     
       
           C   3 = C ( 435   a )+ C ( 420   f )+ C ( 430   d )= C ( 435   c )+ C ( 405   b )+ C ( 420   c )+ C ( 430   a )  Eq. 6 
       
     
     
       
           L   3 = L ( 430   b )= L ( 430   e )  Eq. 7 
       
     
     Eq. 1 shows the equivalent relationship between capacitors  410   a,    410   c,    410   d,  and  410   f.  Eq. 2 shows the equivalent relationship between inductors  410   b  and  410   e.  These equations combine to dictate transmission lines of equal length in the first stage of distributed amplifier  401 . Also relating to the first stage of distributed amplifier  401 , Eq. 3 shows the matching of the capacitance at the input of the first stage ( 415   a  and  410   d ) with the output capacitance of the first stage ( 415   c,    405   a,  and  410   a ). 
     The pattern continues for the number of stages of distributed amplifier  401 . At each stage, the input capacitance is matched with the output capacitance. This number will vary based upon the desired filter characteristics. The resulting distributed amplifier  401  has a response that mimics the filter design that was used to determine the capacitor values C 1 , C 2 , C 3 , etc. and L 1  L 2 , L 3 , etc. Note that the T-model can be similarly used as an alternative to this approach using the Pi-model. 
     FIG. 5 is a flow diagram that illustrates the process of constructing a distributed amplifier based on filter-synthesis techniques. 
     The filter order, response type, bandwidth, and terminating impedances are determined  505  based upon the designer&#39;s desired response characteristics of the distributed amplifier. As understood herein, the filter can be based upon a variety of different filter designs, e.g. Butterworth or Bessel, with the filter characteristics dependent on designer preferences and application. The filter is synthesized  510  using software-based techniques. The success of the synthesis is determined  515 . If the synthesis is successful, the inductor and capacitor values are compiled  525 . If the synthesis is unsuccessful, the pole/zero response is calculated and the inductor and capacitor values are determined through alternative means, e.g. reference tables  520 . 
     The inductor and capacitor values are converted into transmission line lengths and transistor sizes, respectively  530 . The inductances correspond to a particular length of transmission line. The intrinsic capacitance of capacitors is dependent on its fabricated size. At this point, the required information for the successful construction of a distributed amplifier is available and the amplifier can be synthesized  535 . 
     FIGS. 6-7 are circuit diagrams that illustrate implementations, respectively, of a distributed amplifier  600  in a single-ended transmission line mode and a distributed amplifier  700  in a differential transmission line mode. 
     The above embodiments are only illustrative of the principles of this invention and are not intended to limit the invention to the particular embodiments described. Accordingly, various modifications, adaptations, and combinations of various features of the described embodiments can be practiced without departing from the scope of the invention as set forth in the appended claims.