Abstract:
A method and system utilizing a network analyzer and a test controller for measuring scattering parameters (S-parameters) of a microwave device that rapidly switches through a plurality of states. The test controller sends a trigger to the analyzer, which starts a frequency sweep having substantially the same start and stop frequency, and provides the sweep to the device. The analyzer then measures and stores at least one S-parameter of the device and provides the test controller with a trigger. The test controller updates the device to the next state in a predetermined sequence of states and the above steps are iteratively repeated until S-parameters for all of the states in the sequence have been measured.

Description:
FIELD OF THE INVENTION 
       [0001]    The present invention relates to radio-frequency network analyzers. More specifically, the present invention relates to microwave vector network analyzers and a method and a system for an efficient measurement of parameters of microwave devices and similar, especially scattering parameters of two-port or multiport devices. 
       BACKGROUND OF THE INVENTION 
       [0002]    Linear networks, or nonlinear networks operating with signals sufficiently small to cause the networks to respond in a linear manner, can be completely characterized by parameters measured at the network terminals (ports) without regard to the contents of the networks. Once the parameters of a network have been determined, its behavior in any external environment can be predicted, again without regard to the contents of the network. 
         [0003]    Although a network may have any number of ports, network parameters can be explained most easily by considering a network with only two ports, an input port and an output port, like the network shown in  FIG. 1 . 
         [0004]    To characterize the performance of such a network, any of several parameter sets can be used, each of which has certain advantages. Each parameter set is related to a set of four variables associated with the two-port model. Two of these variables represent the excitation of the network (independent variables), and the remaining two represent the response of the network to the excitation (dependent variables). If the network in  FIG. 1  is excited by voltage sources V 1  and V 2 , the network currents I 1  and I 2  will be related by any of the following equations: 
         [0000]    
       
         
               
               
               
               
             
           
               
                   
                   
               
               
                   
                 H-Parameters 
                 Y-Parameters 
                 Z-Parameters 
               
               
                   
                   
               
             
             
               
                   
                 V 1  = h 11 I 1  + h 12 V 2   
                 I 1  = y 11 V 1  + y 12 V 2   
                 V 1  = z 11 I 1  + z 12 I 2   
               
               
                   
                 I 2  = h 21 I 1  + h 22 V 2   
                 I 2  = y 21 V 1  + y 22 V 2   
                 V 2  = z 21 I 1  + z 22 I 2   
               
               
                   
                   
               
             
          
         
       
     
         [0005]    The only difference in the parameter sets is the choice of independent and dependent variables. The parameters are the constants used to relate these variables. 
         [0006]    The above H-parameters can be used as an explanatory example to clarify how parameter sets of this type can be determined through measurement. The parameter h 11  is determined by setting V 2  equal to zero, e.g. by applying a short circuit to the output port of the network. The parameter h 11  is then the ratio of V 1  to I 1 , i.e. the input impedance of the resulting network. The parameter h 12  is in turn determined by measuring the ratio of V 1  to V 2  (i.e. the reverse voltage gain) having the input port open circuited. It is important to note that both open and short circuits are essential for obtaining the above-mentioned H-parameters, Y-parameters and Z-parameters. 
         [0007]    However, the use of said H-, Y- and Z-parameters in connection with higher frequencies, especially in the microwave domain, present a problem since a short circuit looks like an inductor and an open circuit has some leakage capacitance. Active devices such as transistors and tunnel diodes are often instable if short or open circuited. In addition it is difficult to achieve short and open circuits over a broad band of frequencies, which is typically required. Moreover, it is difficult to measure total current or total voltage, which is required when using H-, Y-, or Z-parameters. 
         [0008]    It is obvious that another method has to be used for characterizing these devices at high frequencies, especially microwave frequencies. 
         [0009]    If we embed the exemplifying two-port device in  FIG. 1  into a transmission line, and terminate the transmission line in its characteristic impedance Z L , we can think of the stimulus signal provided by a generator having a impedance Z S  that matches said characteristic impedance as a traveling wave incident on the device, and the response signal as a wave reflecting from the device or being transmitted through the device, see  FIG. 2 . 
         [0010]    We can then establish this new set of equations relating these incident and “scattered” waves: 
         [0000]        E   1r   =S   11   E   1i   +S   12   E   2i   [1] 
         [0000]        E   2r   =S   21   E   1i   +S   22   E   2i   [2] 
         [0011]    Wherein E 1r  and E 2r  are the dependent voltages reflected from the 1st and 2nd ports respectively, whereas E 1i  and E 2i  are the independent voltages incident upon the 1st and 2nd ports respectively. 
         [0012]    Dividing the new set of equations by Z 0  (where Z 0  is the characteristic impedance of the transmission line) we can alter these equations to a more recognizable form: 
         [0000]        b   1   =S   11   a   1   +S   12   a   2   [3] 
         [0000]        b   2   =S   21   a   1   +S   22   a   2   [4] 
         [0013]    Wherein 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       b 
                       n 
                     
                     = 
                     
                       
                         E 
                         nr 
                       
                       
                         
                           Z 
                           0 
                         
                       
                     
                   
                   , 
                   
                       
                   
                    
                   
                     
 
                   
                    
                   and 
                 
               
               
                 
                   [ 
                   5 
                   ] 
                 
               
             
             
               
                 
                   
                     
                       a 
                       n 
                     
                     = 
                     
                       
                         E 
                         ni 
                       
                       
                         
                           Z 
                           0 
                         
                       
                     
                   
                   ; 
                 
               
               
                 
                   [ 
                   6 
                   ] 
                 
               
             
           
         
       
     
         [0000]    and wherein:
   S 11  is the input reflection coefficient equal to b 1 /a 1  with a 2 =0, i.e. no incident wave E 2i , which is accomplished by terminating the output of the two-port in an impedance equal to Z 0 .   S 22  is the output reflection coefficient equal to b 2 /a 2  with a 1 =0, i.e. no incident wave Eli, which is accomplished by terminating the input of the two-port in an impedance equal to Z 0 .   S 21  is the forward transmission (insertion) gain equal to b 2 /a 1  with a 2 =0, i.e. no incident wave E 2i , which is accomplished by terminating the output of the two-port in an impedance equal to Z 0 .   S 12  is the reverse transmission (insertion) gain equal to b 1 /a 2  with a 1 =0, i.e. no incident wave Eli, which is accomplished by terminating the input of the two-port in an impedance equal to Z 0 .   
 
         [0018]    Where, for example: 
         [0000]    |b 1 | 2 =Power reflected from the 1st port; and
 
|a 1 | 2 =Power incident on the 1st port.
 
         [0019]    The above scattering parameters or S-parameters are determined with resistive termination, which obviates the difficulties involved in obtaining the broadband open and short circuit conditions required for the H-, Y-, and Z-parameters. Moreover, parasitic oscillations in active devices are minimized when the device is terminated in resistive loads. There is also standard equipment available for determining S-parameters since only incident wave E ni  and reflected voltages need to be measured. 
         [0020]    S-parameters are conveniently measured by means of modern professional microwave network analyzers, e.g. the Agilent E8362B vector network analyzer from Agilent Technologies Inc. with Head Quarters in Palo Alto, Calif., USA. S-parameters are measured by a modern microwave network analyzer substantially in the same way as indicated above, i.e. by providing a well-defined incident wave E 1i , E 2i  to the device under test and by measuring a possible reflected wave E 1r , E 2r  caused by the incident wave E 1i , E 2i . The conventional way to do this is to provide an incident wave E 1i , E 2i  with a frequency sweep that covers all the frequencies of interest for a certain state of a device under test, and then change the state of the device under test and provide a new frequency sweep. 
         [0021]    However, the number of states that need to be measured tends to be very large when measuring a device that can assume several thousand of different states. An example of such a device is the transmit-and-receive modules (T/R-module) in radar equipments. Such T/R-modules can assume thousands of different states regarding phase and magnitude. Each such state affects the magnitude and/or phase of a signal that is transmitted or a signal that is received by the T/R-module. 
         [0022]    The states in a T/R-module or a similar device under test can be changed very fast compared to changing the frequency in a network analyzer to accomplish a frequency sweep. Typically it takes milliseconds to change the frequency in a network analyzer and just 20-30 μs to change the state in the T/R-modules that are commonly measured today. 
         [0023]    Moreover, it takes time to extract measured data from the microwave network analyzer to an external verification unit in setups comprising a verification unit. Every time communication is established there is also a certain amount of overhead. Depending on the type of instrument and the protocol used the total time for extracting data varies. In the Agilent E8362B the time is typically 30-100 milliseconds. 
         [0024]    The time consumed during frequency change (10-20 ms for each frequency) and data retrieving with a microwave network analyzer (30-100 ms) is multiplied with the number of states that are to be measured. If a lot of states are to be measured this easily takes hours, e.g. when characterizing a T/R-module that may assume more than 600000 states. Such delays are clearly an inconvenience, particularly if a large number of T/R-modules or similar devices are to be characterized, which e.g. may be the case when developing and manufacturing such modules. 
         [0025]    Consequently, there is a need for a method that gives a much faster measurement. 
       SUMMARY OF THE INVENTION 
       [0026]    The invention provides for a method of using a microwave vector network analyzer and a test controller for measuring at least one S-parameter of a microwave device or similar, which device can assume a plurality of states, and which device can switch very fast from one state to another. 
         [0027]    The measuring is achieved by a plurality of steps, which can be described in the following way: The test controller sends a trigger to the analyzer that. When the analyzer receives the trigger it will start a frequency sweep having substantially the same start and stop frequency. In the art a sweep with the same start and stop frequency is often called a zero frequency sweep or a zero span sweep. The frequency sweep is provided to the device under test. The analyzer then executes a measurement of at least one S-parameter of the device under test, stores the S-parameter data from the measurement and provides the test controller with a trigger. The test controller then updates the device under test to the next state in a predetermined sequence of states when it receives the trigger from the analyzer. These steps are repeated until all states in the predetermined sequence of states have been measured. 
         [0028]    By configuring the analyzer to perform a zero frequency sweep or similar it will be possible to e.g. utilize the trigger function associated with a frequency sweep function in the analyzer without actually using any frequency sweep, i.e. without changing the frequency of the signal that is provided to the device. This makes it possible to automate the measuring performed by steps described above. The measuring of the states in a sequence of states according to the steps above is not delayed by any frequency change in the analyzer. The measuring is therefore very fast. 
         [0029]    It is preferred that the S-parameter data obtained by the analyzer during the measurement sequence is transferred to the test controller when all states in the predetermined sequence have been measured. 
         [0030]    It is also preferred that the S-parameter data is transferred to the test controller via a fast local area network (LAN). 
         [0031]    In addition, the invention provides for a system for measuring at least one S-parameter of a microwave device or similar, which system comprises a test controller a network analyzer and the microwave device itself. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0032]      FIG. 1  shows a schematic illustration of a well-known two-port network having one input port and one output port. 
           [0033]      FIG. 2  shows the exemplifying two-port device in  FIG. 1  embedded in a transmission line that is terminated in its characteristic impedance Z L  at one end and connected at the other end to a generator with an impedance Z G  that matches said characteristic impedance. 
           [0034]      FIG. 3  shows an exemplifying measuring system  100  for measuring S-parameters according to an embodiment of the present invention. 
           [0035]      FIG. 4  shows an exemplifying flowchart of the measuring sequences that can be performed according to an embodiment of the present invention. 
       
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
       [0036]    The present invention will now be described in more detail with reference to protected systems according to various embodiments of the invention. 
         [0037]      FIG. 3  shows an exemplifying measuring system  100  for measuring S-parameters in a radio-frequency (RF) device according to a preferred embodiment of the present invention. The exemplifying system  100  comprises a verification unit  10 , a microwave network analyzer  20 , a power and logic unit  30  and a device under test  40 . 
       The Units in the Measuring System 
       [0038]    The verification unit  10  in  FIG. 3  is preferably an ordinary personal computer (PC) that is generally available on the market, possibly with slight hardware modifications such as adding an I/O-card for facilitating the communication with peripheral equipment etc. It is also preferred that the PC is provided with software adapted for measuring and evaluation. Other verification units or similar are clearly possible, e.g. customized or dedicated verification units. 
         [0039]    It is preferred that the verification unit  10  comprises a preprogrammed definition of the specific states that the device under test  40  shall assume during a measurement. In addition it is preferred that the verification unit  10  comprises a preprogrammed configuration of the measurement sequence that shall be performed during the measurement. The configuration of the measurement sequence may e.g. define the order in which the defined states shall be assumed by the device under test  40 . 
         [0040]    It is also preferred that the verification unit  10  comprises a preprogrammed configuration of the microwave network analyzer  20  that is to be used during a measurement. A typical configuration of a microwave network analyzer  20  includes such parameters as the S-parameter(s) to be measured, the frequency or frequencies of the incident wave(s) E 1i , E 2i , the power level of the incident wave(s) E 1i , E 2i , the trigger(s) that shall be used during the measurement, the number of measurements to be performed, etc. The configuration of a microwave network analyzer may differ between various analyzers and the configuration may also differ between various measuring setups. Hence, more parameters and other parameters may be needed to configure a specific microwave network analyzer  20 . 
         [0041]    If we now turn the attention to the microwave network analyzer  20  in  FIG. 3  it is preferred that the analyzer is an Agilent E8362 microwave vector network analyzer or similar. However, the invention is not limited to an Agilent E8362. On the contrary, other analyzers with similar properties or at least suitable properties can be used. The analyzer may also cover other parts of the radio-frequency spectrum in addition to the microwave spectrum. 
         [0042]    When it comes to the power and logic unit  30  in  FIG. 3  it can be regarded as an interface between the verification unit  10  and the device under test  40 . It is preferred that the power and logic unit  30  controls the device under test  40  according to instructions received from the verification unit  10 . However, other embodiments of the invention may have a power and logic unit  30  that controls the device under test  40  in a more or less autonomous manner, i.e. partly or fully without instructions from the verification unit  10 . It is moreover preferred that the power and logic unit  30  provides the device under test  40  with the necessary electric power and similar that is required for a proper function of the device under test  40 . The power and logic unit  30  can be a separate unit, or a unit that is partly arranged in the verification unit  10 , or a unit that is fully arranged in the verification unit  10 . The verification unit  10  and the power and logic unit  30  are identified as the test-controller  10 ,  30 , when they are referred to as one single functional unit, which however may be implemented as several physical units. 
         [0043]    As regards the microwave device under test  40  in  FIG. 3  it is a two-port microwave device with an input port and an output port. However, other devices are clearly possible, e.g. a multi-port device or similar. The microwave device under test  40  can assume a large number of different states and the shift from one state to another can be executed very quickly, e.g. In the range of 10-20 μs. The device under test  40  may e.g. be a radar T/R-module that can assume thousands of different states of phase and magnitude, which states affect the magnitude and/or phase of a signal that is transmitted or a signal that is received by the T/R-module. 
       Connecting the Units 
       [0044]    The verification unit  10  in  FIG. 3  is connected to the power and logic unit  30  for enabling an exchange of data and control signals between the units  10 ,  30 . The connection may e.g. be of any suitable kind that is commonly used to connect a personal computer (PC) to an external device. 
         [0045]    The power and logic unit  30  in  FIG. 3  is in turn connected to the device under test  40  for enabling an exchange of data, control signals and power etc. The connection is typically a customized or a dedicated connection that is adapted to enable a simple and efficient control of the device under test  40 , e.g. enable the power and logic unit  30  to simply and quickly command the device under test  40  to change its state. It is also preferred that the connection in question provides the device under test  40  with the required power if needed. 
         [0046]    The verification unit  10  in  FIG. 3  is moreover connected to the microwave network analyzer  20  for enabling an exchange of information and control signals between the units  10 ,  40 . The information is typically data that has been obtained by the microwave network analyzer  20  during a measurement of the device under test  40 . Control signals are typically needed to establish each communication session between the units  10 ,  40 . Headers and similar in the data packages or similar that are transferred from the microwave network analyzer  20  to the verification unit  10  may also be regarded as control signals. The amount of data that is transferred is typically large, which means that the transfer is time-consuming. The control signals add to this time. Depending on the type of microwave network analyzer  20  and the protocol used the total time for extracting data from the analyzer  20  varies. In the case of an Agilent E8362B the time for transfer a set of measured data to the verification unit  10  is typically 30-100 milliseconds. To minimize the amount of time for transferring data from the microwave network analyzer  20  to the verification unit  10  it is preferred that the verification unit  10  is connected to the microwave network analyzer  20  via a high-speed channel, e.g. a local area network (LAN), e.g. a network using Ethernet or similar. It is moreover preferred that the connection is a per-to-per connection, i.e. that no other device is using the high-speed connection, since this may cause delays in the case of congestions on the channel. It is also preferred that the data is transferred as directly as possible from the data storage in the microwave network analyzer  20  to the verification unit  10 . This is preferably accomplished by a direct access to the hardware memory circuits in the network analyzer  20 . In the case of an Agilent E8362B this can be achieved by utilizing the DCOM communication protocol. 
         [0047]    The microwave network analyzer  20  in  FIG. 3  is in turn connected to the device under test  40  via two microwave cables, e.g. two coaxial cables. One of the cables connects the microwave network analyzer  20  to the input port of the device under test  40  and the other cable connects the microwave network analyzer  20  to the output port of the device under test  40 . Other connections are clearly possible, e.g. if only one port is to be measured or if the device under test  40  is a multi port device etc. 
         [0048]    The microwave network analyzer  20  and the power and logic unit  30  are also connected to each other via two trigger channels. A first trigger channel enables the power and logic unit  30  to send a trigger to the microwave network analyzer  20  each time the setting of the device under test  40  has changed from one state to another, e.g. each time the power and logic unit  30  has commanded the device under test  40  to assume a new state with respect to phase and magnitude. This trigger has been schematically illustrated in  FIG. 3  by a line with an arrow extending from the power and logic unit  30  to the microwave network analyzer  20 . A second trigger channel enables the microwave network analyzer  20  to send a trigger to the power and logic unit  30  each time the microwave network analyzer  20  has performed a measurement. This trigger has been schematically illustrated in  FIG. 3  by a line with an arrow extending from the microwave network analyzer  20  to the power and logic unit  30 . 
       The Operation of the System 
       [0049]      FIG. 4  shows an exemplifying flowchart of the measuring steps that is performed according to a preferred embodiment of the present invention. 
         [0050]    The first step (A) is to calibrate the microwave network analyzer  20 . The calibration is intended to eliminate the influence from the two microwave cables and possible other arrangements that connect the microwave network analyzer  20  to the device under test  40 . The calibration may also include the internal calibration of the microwave network analyzer  20  and a possible calibration of other units in the measuring system  100 . 
         [0051]    The second step (B) is to load the power and logic unit  30 . In this step it is preferred that the verification unit  10  provides the power and logic unit  30  with a number of preprogrammed states that the device under test  40  shall assume during the measurement. It is also preferred that the verification unit  10  provides the power and logic unit  30  with a preprogrammed configuration of the measurement sequence. The configuration of the measurement sequence may e.g. define the order in which the power and logic unit  30  shall command the device under test  40  to assume the preprogrammed states. The configuration of the measurement sequence may also define how many times the measurement sequence should be executed etc. 
         [0052]    The third step (C) is to configure the microwave network analyzer  20 . In this step it is preferred that the verification unit  10  provides the microwave network analyzer  20  with a preprogrammed configuration. However, it is also possible to have the microwave network analyzer  20  configured manually, e.g. via the keypad on the microwave network analyzer  20  or in some other suitable way. 
         [0053]    The fourth step (D) is to initiate the measurement sequence as defined in step (B). It is preferred that the sequence is initiated by providing the power and logic unit  30  with a start signal or similar. A start signal may e.g. be provided manually or from the verification unit  10  or in some other suitable way. When the power and logic unit  30  receives the start signal it will command the device under test  40  to assume the first state in the measurement sequence. 
         [0054]    The fifth step (E) is to initiate the microwave network analyzer  20 . In this step it is preferred that the power and logic unit  30  provides the microwave network analyzer  20  with a “next state ready” trigger when the device under test  40  has assumed the state that was commanded by the power and logic unit  30  in the previous step. The trigger is preferably provided via the first trigger channel or similar as described above. 
         [0055]    The sixth step (F) is to let the microwave network analyzer  20  measure one measurement point, store the measured S-parameter data and send a “measurement ready” trigger to the power and logic unit  30 . The trigger is provided via the second trigger channel or similar as described above. The measurement is performed by letting the microwave network analyzer  20  provide an incident wave E 1i  or E 2i  of a predefined zero frequency sweep to the device under test  40  and send a trigger to the power and logic unit  30  when the measurement is completed. The zero frequency sweep has substantially the same start and stop frequency, i.e. the incident wave E 1i  or E 2i  has substantially one and the same frequency. In other words the microwave network analyzer  20  does not change the frequency of the incident wave E 1i  or E 2i  to cover any frequency interval. In an Agilent E8362B vector network analyzer this can be achieve by utilizing its “step-sweep mode”. 
         [0056]    There is consequently no delay due to frequency changes in the microwave network analyzer  20  before the next measuring step (i.e. step (G)) can be performed. Similarly, there is no delay due to frequency changes in the microwave network analyzer  20  before the device under test  40  can assume the next state (i.e. proceed from step (G) to step (H)). 
         [0057]    It should be added that a measurement point consequently corresponds to a measurement of the S-parameter(s) for one state of the device under test  40  at one frequency for the incident wave E 1i  or E 2i . A measurement sequence comprises a plurality of such measurement points. 
         [0058]    The number of states to be measured is preferably defined in the preprogrammed definition of the specific states that the device under test  40  shall assume, which definition is comprised by the verification unit  10  and provided to the power and logic unit  30  according to step (B) above. The number of measurement points to be measured by the microwave network analyzer  20  is preferably defined in the preprogrammed configuration that is provided to the microwave network analyzer  20  in step (C) above. The number of states should be equal to the number of measurement points. 
         [0059]    The seventh step (G) is to check if the device under test  40  has assumed the last step in the measurement sequence. The power and logic unit  30  preferably performs the check. 
         [0060]    The execution of the measuring steps will proceed to the eighth step (H), provided that the last step in the measurement sequence has not been reached. In this step it is preferred that the power and logic unit  30  updates the device under test  40  to assume the next step in the measurement sequence. The execution of the measuring steps will then proceed from the fifth step (E) and forward. 
         [0061]    However, the execution of the measuring steps will proceed to the ninth step (I) if the last step in the measurement sequence has been reached. In this step it is preferred that verification unit  10  retrieves or is provided with the data from the measurement sequence that is stored in the microwave network analyzer  20 . In other words, the S-parameter data that has been obtained by the microwave network analyzer  20  during a measurement sequence is transferred to the verification unit  10  when the measurement sequence is completed, i.e. no data is transferred after the individual measurement points or at any other instance in a proceeding measurement sequence. This saves time due to the reduced number of occasions when a communication has to be established between the verification unit  10  and the microwave network analyzer  20 . It is preferred that the microwave network analyzer  20  is configured to provide the verification unit  10  with the S-parameter data when the last measurement point in the measurement sequence has been measured. 
         [0062]    The tenth step (J) is to check if the last measurement sequence has been completed. As pointed out above, the configuration of a measurement sequence may e.g. define that a measurement sequence shall be executed a number of times. It is preferred that the power and logic unit  30  performs this check. 
         [0063]    The execution of the measuring steps will proceed from step (B) or step (C) and forward if the last measurement sequence has not been completed. If the execution of the measuring steps proceeds from step (B) it will be possible to change the configuration of the measurement sequence and the states therein before the next measurement starts. It will also be possible to change the configuration of the microwave network analyzer  20 , as the execution of the measuring steps will pass step (C). However, if the execution of the measuring steps proceeds from step (C) it will only be possible to change the configuration of the microwave network analyzer  20  before the next measurement starts. 
         [0064]    However, the execution of the measuring steps will stop if the last measurement sequence has been completed. 
         [0065]    It should be emphasized that the steps A-J described above is a preferred embodiment of the invention. Other embodiments may not use all these steps and/or may use additional step and/or alternatives to the steps A-J. It should also be emphasized that different embodiments of the invention may execute the measuring steps (e.g. step A-J) in a different sequence, i.e. the order in which the steps are executed may be changed without departing from the invention. 
         [0066]    While the above description comprises exemplifying embodiments of the present invention, it will be appreciated that the invention is susceptible to modification, variation and change without departing from the proper scope or fair meaning of the accompanying claims. 
       REFERENCE SIGNS 
       [0000]    
       
           100  Measuring system 
           10  Verification Unit (VCU) 
           20  Professional Microwave Network Analyzer (PNA) 
           30  Power and Logic Unit (PLU) 
           40  Device Under Test (DUT)