Abstract:
A multi-stage amplifier is provided that uses tunable transmission lines, as well as a calibration method for the multi-stage amplifiers. A multi-stage amplifier, comprises a plurality of tunable amplification stages, wherein each of the tunable amplification stages comprises a tunable resonator based on a transmission line having a tunable element. The tunable elements may vary a capacitance or an inductance to tune a frequency of an applied signal. A calibration method is provided for a multi-stage amplifier having a plurality of transmission lines, an input stage and an output stage. The multi-stage amplifier is calibrated by generating a signal to determine a frequency for a substantially maximum power; generating an error signal by comparing the frequency for the substantially maximum power with a desired frequency; varying a digital control code applied to each of the tunable transmission lines, input stage and output stage until the error signal satisfies predefined criteria.

Description:
STATEMENT OF GOVERNMENT RIGHTS 
       [0001]    This invention was made with Government support under Contract No.: FA8650-09-C-7924 (Defense Advanced Research Projects Agency (DARPA)). The Government has certain rights in this invention. 
     
    
     FIELD OF THE INVENTION 
       [0002]    The present invention relates generally to amplifiers capable of operating at millimeter-wave (mm-wave) frequencies, and more specifically to multi-state amplifiers based on tunable transmission lines. 
       BACKGROUND 
       [0003]    Low noise amplifiers (LNAs) are the building blocks of any communication system. For example, a low-noise amplifier is typically the first active circuit after the antenna in a radio transceiver, and is thus a critical building block for a radio transceiver. To increase receiver sensitivity and reduce the amount of noise contributed by subsequent stages, the LNA is required to have a moderate gain and a low-noise figure. The LNA is required to be matched to the characteristic impedance of the system (usually 50 ohms) at its input and output. In addition, to operate at millimeter-wave (mm-wave) frequencies (30 GHz and higher), such systems must often be capable of transmitting, receiving and manipulating mm-wave signals. 
         [0004]    As MOSFET miniaturization reaches deep submicron sizes (0.5 mm and below), mm-wave LNAs and other amplifiers require multi-stage designs to achieve the necessary gain. Due to process variations, model inaccuracies and the extra parasitics related to wiring, however, the various stages will typically operate at different frequencies. As a result, the total gain decreases and the bandwidth of the amplifier will change. In addition, the frequency response of the amplifier (S 21 ) exhibits a frequency shift and the input/output matching will be impaired. For lower frequencies, such as microwave frequencies, tunable varactors can be used. A varactor has a capacitance that varies with the applied voltage. At mm-wave frequencies, however, varactors have a low quality factor. Therefore, varactors cannot be used at mm-wave frequencies for varying the capacitance. 
         [0005]    U.S. patent application Ser. No. 13/251256, filed 02 Oct. 2011, entitled “Structure and Modeling of Variable Transmission Lines,” discloses a tunable transmission line that is digitally tuned to compensate for process variations in both the active and passive devices of the RF design. A disclosed variable transmission line comprises a semiconductor substrate, a signal line, a first plurality of capacitor ports below the signal line, where each capacitor port is operative to be connected to either ground or a floating potential, a bottom ground plane and one or more side shield wires. 
         [0006]    A need remains for a digitally controlled resonator for resonant amplifiers based on a tunable passive component. A further need exists for a multi-stage digitally controlled resonator for resonant amplifiers where the amplification stages are identical and working at the same resonant frequency that can be controlled in a digital manner. Yet another need exists for a method to employ the resonator in the digital calibration of the frequency response of the amplifiers. 
       SUMMARY 
       [0007]    Generally, a multi-stage amplifier is provided that uses tunable transmission lines. A frequency response calibration technique is also provided. According to one aspect of the invention, a multi-stage amplifier, comprises a plurality of tunable amplification stages, wherein each of the tunable amplification stages comprises a tunable resonator based on a transmission line having a tunable element. The tunable elements may vary a capacitance or an inductance to tune a frequency of an applied signal. 
         [0008]    According to another aspect of the invention, a calibration method is provided for a multi-stage amplifier having a plurality of transmission lines, an input stage and an output stage. The multi-stage amplifier is calibrated by generating a signal to determine a frequency for a substantially maximum power; generating an error signal by comparing the frequency for the substantially maximum power with a desired frequency; varying a digital control code applied to the tunable transmission lines until the error signal satisfies a first predefined criteria; varying a digital control code applied to the input stage until the error signal satisfies a second predefined criteria; and varying a digital control code applied to the output stage until the error signal satisfies a third predefined criteria. 
         [0009]    A more complete understanding of the present invention, as well as further features and advantages of the present invention, will be obtained by reference to the following detailed description and drawings. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0010]      FIG. 1  illustrates a multi-stage low noise amplifier incorporating features of the present invention; 
           [0011]      FIG. 2  illustrates an exemplary model of a tunable amplification stage that may be employed by the present invention; 
           [0012]      FIG. 3  illustrates a frequency response for the three exemplary tunable transmission lines of  FIG. 1 , for an exemplary small band design; 
           [0013]      FIG. 4  illustrates a frequency response for the three exemplary tunable transmission lines of  FIG. 1 , for an exemplary broadband design; 
           [0014]      FIG. 5  illustrates an alternate multi-stage low noise amplifier incorporating features of the present invention; 
           [0015]      FIG. 6  illustrates the frequency response for the alternate multi-stage low noise amplifier of  FIG. 5   
           [0016]      FIG. 7  illustrates an alternate multi-stage low noise amplifier having on-chip digital calibration in accordance with the present invention; 
           [0017]      FIG. 8  is exemplary pseudo code for a digital self-calibration process for the exemplary multi-stage low noise amplifier; 
           [0018]      FIG. 9  is a flow chart describing an exemplary implementation of an algorithm for finding the frequency for maximum output power; 
           [0019]      FIG. 10  illustrates a single stage variable transmission line low noise amplifier in accordance with the present invention; 
           [0020]      FIG. 11  illustrates a three stage variable transmission line low noise amplifier in accordance with the present invention; and 
           [0021]      FIG. 12  illustrates an alternate single stage hybrid variable transmission line low noise amplifier  1200  in accordance with the present invention. 
       
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
       [0022]    The present invention provides a digitally controlled resonator for resonant amplifiers based on a tunable passive component, such as a tunable capacitor or inductor. According to one aspect of the invention, a multi-stage digitally controlled resonator for resonant amplifiers employs tunable amplification stages that can optionally be tuned to work at substantially the same resonant frequency. According to another aspect of the invention, the disclosed resonator is employed to calibrate the frequency response of the amplifiers. 
         [0023]      FIG. 1  illustrates a multi-stage low noise amplifier  100  incorporating features of the present invention. As shown in  FIG. 1 , the multi-stage low noise amplifier  100  comprises a plurality of tunable amplification stages  120 - 1  through  120 -N, discussed further below, for example, in conjunction with  FIG. 2 . In the exemplary embodiment of  FIG. 1 , N is equal to 3. As discussed hereinafter, each tunable amplification stage  120  comprises a tunable passive component, such as a tunable capacitor or inductor, that can optionally be tuned to work at substantially the same resonant frequency as each other. The stages are substantially identical. In addition, the multi-stage low noise amplifier  100  comprises an input stage  110  and an output stage  130  that are substantially matched. 
         [0024]    As shown in  FIG. 1  and discussed more fully below in conjunction with  FIGS. 3 and 4 , a given tunable amplification stage  120 - i  has a corresponding tunable resonant frequency f i . 
         [0025]      FIG. 2  illustrates an exemplary model of a tunable amplification resonator stage  120  that may be employed by the present invention. As shown in  FIG. 2 , the exemplary tunable amplification resonator stage  120  comprises two transmission lines L 1  and L 2  together with a tunable transmission line-stub C 2 . The transmission lines L 1  and L 2  may be implemented, for example, using microstrip or coplanar waveguides. (See, e.g., Yanyu Jin et al., “A Wideband Millimeter-Wave Power Amplifier With 20 dB Linear Power Gain and +8 dBm Maximum Saturated Output Power,” IEEE J. of Solid-States Circuits, vol. 43, pp. 1553-1562, 2008, incorporated by reference herein) together with a tunable transmission line stub C 2 . A parallel capacitance C 1  comprises the active device output capacitance and the wiring capacitance, in a known manner. 
         [0026]    The tunable transmission line stub C 2  may be a tunable capacitor with a controllable resonance frequency, such as those described in U.S. patent application Ser. No. 13/251256, filed 02 Oct. 2011, entitled “Structure and Modeling of Variable Transmission Lines,” incorporated by reference herein. In an alternate implementation, the tunable resonator can be realized with elements L 1  and L 2  operating (both or only L 1 /L 2 ) as a tunable inductor with a controllable resonance frequency, such as those described in U.S. patent application Ser. No. 12/478385, filed 04 Jun. 2009, entitled “Vertical Coplanar Waveguide With Tunable Characteristic Impedance, Design Structure and Method of Fabricating the Same,” and/or U.S. patent application Ser. No. 12/911327, filed 25 Oct. 2010, entitled “&#39;On-Chip Tunable Transmission Lines, Methods of Manufacture and Design Structures,”each incorporated by reference herein. The input impedance, Z in (s), of each tunable amplification stage  120  can be expressed as follows: 
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         [0027]      FIG. 3  illustrates the frequency response  300  for the three exemplary tunable transmission lines  120  of  FIG. 1 , for an exemplary small band design. In particular,  FIG. 3  illustrates the power gain between the input and output ports of the tunable transmission lines  120  (s parameter S 21 ), as a function of frequency. As shown in  FIG. 3 , for a small band design, it is desired that the three exemplary tunable transmission lines  120  operate at substantially the same required resonant frequency, f required . The nominal operating frequency, f 0 , of each tunable transmission line  120  is adjusted in accordance with one embodiment of the present invention to be aligned to the desired required frequency, f required  (Δf=f 0 −f required ). In the small band embodiment, the three stages  120  are substantially identical. Thus, as discussed further below, the digital code applied to each stage  120  can be identical and the frequency shift for each stage  120  is the same. By changing the capacitance of the variable transmission line, the resonance frequency of each resonant stage  120  changes, and the design can be centered back to the required frequency f required . 
         [0028]      FIG. 4  illustrates the frequency response  400  for the three exemplary tunable transmission lines  120  of  FIG. 1 , for an exemplary broadband design. In particular,  FIG. 4  illustrates the power gain between the input and output ports of the tunable transmission lines  120  (s parameter S 21 ), as a function of frequency. As shown in  FIG. 4 , for a broadband design, it is desired that the three exemplary tunable transmission lines  120  operate at different resonant frequencies, f 1  through f 3 . For the broadband embodiment, additional bandwidth is obtained at the expense of gain. In the broadband embodiment, the resonant frequencies, f 1  through f 3 , of the stages  120  are staggered and working at three different frequencies: f 1 , f 2  and f 3 . In this case, each stage  120  can be tuned individually at the desired frequency, resulting in a frequency transfer with larger bandwidth and possible ripple in the pass-band, as shown in  FIG. 4 . 
         [0029]      FIG. 5  illustrates an alternate multi-stage low noise amplifier  500  incorporating features of the present invention. As shown in  FIG. 5 , the multi-stage low noise amplifier  500  comprises a plurality of tunable amplification stages  520 - 1  through  120 -N, in a similar manner to  FIG. 1 . In addition, the multi-stage low noise amplifier  500  of  FIG. 5  employs tunable transmission lines, such as those described above in conjunction with  FIG. 2 , as the input stage  510  and output stage  530 , for input and output matching. 
         [0030]    Generally, the input/output matching embodiment of  FIG. 5  aims to change the frequency of the tunable transmission lines for the best match to 50 ohms, without altering the gain setting of the amplifier  500 . This can be achieved, for example, with a high input/output isolation for the individual stages. 
         [0031]      FIG. 6  illustrates the frequency response  600  for the alternate multi-stage low noise amplifier  500  of  FIG. 5 . In particular,  FIG. 6  illustrates the input reflection coefficient, S 11 , and output reflection coefficient, S 22 , of the input and output tunable transmission lines  510  and  530 , respectively, as a function of frequency. As shown in  FIG. 6 , for the input/output matching design, it is desired that the exemplary input and output tunable transmission lines  510  and  530  operate at substantially the same required resonant frequency, f required . The nominal operating frequency, f 0 , of each tunable transmission line  510 ,  530  is adjusted in accordance with one embodiment of the present invention to be aligned to the desired required frequency, f required  (Δf=f 0 −f required ). By changing the capacitance of the variable transmission lines  510 ,  530 , the resonance frequency of each transmission line  510 ,  530  changes, and the design can be centered back to the required frequency f required . 
         [0032]    Digital Calibration of Multi-Stage Low Noise Amplifier 
         [0033]      FIG. 7  illustrates an alternate multi-stage low noise amplifier  700  having on-chip digital calibration in accordance with the present invention. As shown in  FIG. 7 , the multi-stage low noise amplifier  700  comprises a plurality of tunable amplification stages  7 - 1  through  720 -N, in a similar manner to  FIG. 1 . In addition, the multi-stage low noise amplifier  700  employs tunable transmission lines as the input stage  710  and output stage  730 , for input and output matching, in a similar manner to  FIG. 5 . 
         [0034]    In addition, the exemplary multi-stage low noise amplifier  700  comprises a voltage controlled oscillator (VCO)  740 , a state machine  750  and a power detector  760 . As discussed further below, the VCO  740  can sweep its output frequency and the state machine  750  monitors its frequency to generate an RF signal, f RF , that is used during calibration. The state machine  750  is discussed further below in conjunction with  FIGS. 8 and 9 . The power detector  760  measures the power during calibration at the output of the output matching stage  730 . During self calibration, the input/output match  710 ,  730  and the gain of the tunable transmission lines  720  will be changed by the state machine  740 , for example, using six bits of digital control. Generally, the input and output match can be measured on a vector network analyzer (VNA) and the capacitance of the input and output variable transmission line stub is changed for the best match at the required frequency, using external measurement equipment. In the state machine  740 , a low frequency analog-to-digital converter (ADC) (e.g., 10-bit successive approximation or SAR) can measure the DC value given by the power detector  750 . 
         [0035]      FIG. 8  is exemplary pseudo code for a digital self-calibration process  800  for the exemplary multi-stage low noise amplifier  700 . As shown in  FIG. 8 , the digital self-calibration process  800  comprises the steps of: 
         [0036]    1. Sweep RF frequency and find the frequency for maximum power (f max ) using the algorithm  900  described in  FIG. 9 ; 
         [0037]    2. Compare frequency f max  with the desired frequency f required  and generate an error signal Δf=|f max −f required |. 
         [0038]    3. Generate a digital code for controlling the variable transmission lines  720  in the resonator stage. 
         [0039]    4. Repeat Steps 1, 2 and 3 until Δf is below a predefined threshold specified by desired frequency accuracy. 
         [0040]    5. Change input matching and repeat Steps 1,2 and 3 (this time controlling only the code for the input transmission line  710 ). 
         [0041]    6. Change output matching and repeat 1,2 and 3 (this time controlling only the code for the output transmission line  730 ). 
         [0042]      FIG. 9  is a flow chart describing an exemplary implementation of an algorithm  900  for finding the frequency for maximum output power. As shown in  FIG. 9 , a counter, n, and the initial frequency of the RF signal, f RF , are initialized during step  910 . The power is measured during step  920 , and saved during step  930 . A test is performed during step  940 , to determine if the counter has reached the maximum value, N. If it is determined during step  940  that the counter has reached the maximum value, N, then the maximum output power is determined during step  950 . If, however, it is determined during step  940  that counter has not reached the maximum value, N, then the counter is incremented at step  960 , the power re-measured at step  970  and saved at step  980 . 
         [0043]    A further test is performed during step  990 , to determine if the current power exceeds the prior power measurement. If so, the value is stored during step  995 . 
         [0044]      FIG. 10  illustrates a single stage variable transmission line low noise amplifier  1000  in accordance with the present invention. As shown in  FIG. 10 , the variable transmission line LNA  1000  is based on a cascode amplifier with the transmission lines TL 1  and TL 2  for the input match. A tunable transmission line TL 4  between the common-source and common-gate transistor increases the gain at the resonance frequency by resonating with the gate-source capacitance of M 3  and the stray capacitance at the drain of M 1 . The gate of M 3  is at V DD  (RF ground) and its drain is connected to the resonator  1010 . 
         [0045]    The resonator  1010  consists of two transmission lines TL 5  and TL 6  with a variable transmission line stub  1020  connected in the middle of transmission lines TL 5  and TL 6 . As shown in  FIG. 10 , a 6-bit control vector can be applied to the resonator  1010  to change the capacitance of the stub  1020 . The code can be, for example, a thermometer code (switching equal capacitance when incrementing the code by one) with the following values: 
         [0046]    {000000, 000001, 000011, 000111, 001111, 011111, 111111}. 
         [0047]    The cascode stage  1030  is biased at constant current L using a current source from the transistor M 2 . For best matching, transistor M 2  has a transmission line TL 3  substantially identical to transmission line TL 2  in its source. A resistor R 1  works as a choke for the input RF signal and C 2  provides low-pass filtering for the RF signal coming from the RF path, preventing RF pollution through supply lines. The same capacitor C 2  together with resistor R 2  provides low-pass filtering for any RF signal/noise coming from the current source L. 
         [0048]      FIG. 11  illustrates a three stage variable transmission line low noise amplifier  1100  in accordance with the present invention. As shown in  FIG. 11 , the exemplary variable transmission line LNA stage  1100  comprises three stages  1120 - 1  through  1120 - 3  each comprising a variable transmission line  1125 - 1  through  1125 - 3 , respectively. In addition, the exemplary variable transmission line LNA stage  1100  employs variable transmission lines in an input stage  1110  and an output stage  1130 . Finally, the exemplary variable transmission line LNA stage  1100  employs a common bias circuit  1140  for all three stages  1120 . 
         [0049]      FIG. 12  illustrates an alternate single stage hybrid variable transmission line low noise amplifier  1200  in accordance with the present invention. As shown in  FIG. 12 , the hybrid variable transmission line LNA  1200  is based on a cascode amplifier with the transmission lines of  FIG. 10  replaced with inductors. Inductors L 1  and L 2  provide the input match. An inductor L 4  between the common-source and common-gate transistor increases the gain at the resonance frequency by resonating with the gate-source capacitance of M 3  and the stray capacitance at the drain of M 1 . The gate of M 3  is at V DD  (RF ground) and its drain is connected to the resonator  1210 . 
         [0050]    The resonator  1210  consists of a variable transmission line  1220  connected at the drain of M 3  and an inductor L 5 . As shown in  FIG. 12 , a 6-bit control vector can be applied to the resonator  1210  to change the capacitance of the stub. The code can be, for example, a thermometer code (switching equal capacitance when incrementing the code by one) with the following values: 
         [0051]    {000000, 000001, 000011, 000111, 001111, 011111, 1111111}. 
         [0052]    The cascode stage  1230  is biased at constant current I o  using a current source from the transistor M 2 . For best matching, transistor M 2  has an inductor L 3  substantially identical to inductor L 2  in its source. A resistor R 1  works as a choke for the input RF signal and C 2  provides low-pass filtering for the RF signal coming from the RF path, preventing RF pollution through supply lines. The same capacitor C 2  together with resistor R 2  provides low-pass filtering for any RF signal/noise coming from the current source I o . 
         [0053]    Thus, the functions of the present invention can be embodied in the form of methods and apparatuses for practicing those methods. One or more aspects of the present invention can be embodied in the form of program code, for example, whether stored in a storage medium, loaded into and/or executed by a machine, or transmitted over some transmission medium, wherein, when the program code is loaded into and executed by a machine, such as a computer, the machine becomes an apparatus for practicing the invention. When implemented on a general-purpose processor, the program code segments combine with the processor to provide a device that operates analogously to specific logic circuits. The invention can also be implemented in one or more of an integrated circuit, a digital signal processor, a microprocessor, and a micro-controller. 
       Exemplary System and Article of Manufacture Details 
       [0054]    As will be appreciated by one skilled in the art, aspects of the present invention may be embodied as a system, method or computer program product. Accordingly, aspects of the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment (including firmware, resident software, micro-code, etc.) or an embodiment combining software and hardware aspects that may all generally be referred to herein as a “circuit,” “module” or “system.” Furthermore, aspects of the present invention may take the form of a computer program product embodied in one or more computer readable medium(s) having computer readable program code embodied thereon. 
         [0055]    One or more embodiments of the invention, or elements thereof, can be implemented in the form of an apparatus including a memory and at least one processor that is coupled to the memory and operative to perform exemplary method steps. One or more embodiments can make use of software running on a general purpose computer or workstation. Such an implementation might employ, for example, a processor, a memory, and an input/output interface formed, for example, by a display and a keyboard. The term “processor” as used herein is intended to include any processing device, such as, for example, one that includes a CPU (central processing unit) and/or other forms of processing circuitry. Further, the term “processor” may refer to more than one individual processor. The term “memory” is intended to include memory associated with a processor or CPU, such as, for example, RAM (random access memory), ROM (read only memory), a fixed memory device (for example, hard drive), a removable memory device (for example, diskette), a flash memory and the like. 
         [0056]    Accordingly, computer software including instructions or code for performing the methodologies of the invention, as described herein, may be stored in one or more of the associated memory devices (for example, ROM, fixed or removable memory) and, when ready to be utilized, loaded in part or in whole (for example, into RAM) and implemented by a CPU. Such software could include, but is not limited to, firmware, resident software, microcode, and the like. 
         [0057]    Aspects of the present invention are described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and/or block diagrams, and combinations of blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks. 
         [0058]    These computer program instructions may also be stored in a computer readable medium that can direct a computer, other programmable data processing apparatus, or other devices to function in a particular manner, such that the instructions stored in the computer readable medium produce an article of manufacture including instructions which implement the function/act specified in the flowchart and/or block diagram block or blocks. 
         [0059]    The computer program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other devices, such as a state machine, to cause a series of operational steps to be performed on the computer, other programmable apparatus or other devices to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide processes for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks. 
         [0060]    Method steps described herein may be tied, for example, to a general purpose computer programmed to carry out such steps, or to hardware for carrying out such steps, as described herein. Further, method steps described herein, including, for example, obtaining data streams and encoding the streams, may also be tied to physical sensors, such as cameras or microphones, from whence the data streams are obtained. 
         [0061]    In any case, it should be understood that the components illustrated herein may be implemented in various forms of hardware, software, or combinations thereof; for example, application specific integrated circuit(s) (ASICS), state machines, functional circuitry, one or more appropriately programmed general purpose digital computers with associated memory, and the like. Given the teachings of the invention provided herein, one of ordinary skill in the related art will be able to contemplate other implementations of the components of the invention. 
         [0062]    The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used herein, the singular forms “a”, “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “comprises” and/or “comprising,” when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. 
         [0063]    The corresponding structures, materials, acts, and equivalents of all means or step plus function elements in the claims below are intended to include any structure, material, or act for performing the function in combination with other claimed elements as specifically claimed. The description of the present invention has been presented for purposes of illustration and description, but is not intended to be exhaustive or limited to the invention in the form disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the invention. The embodiment was chosen and described in order to best explain the principles of the invention and the practical application, and to enable others of ordinary skill in the art to understand the invention for various embodiments with various modifications as are suited to the particular use contemplated.