Classifications

• • H—ELECTRICITY
  • H03—ELECTRONIC CIRCUITRY
  • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
  • H03H17/00—Networks using digital techniques
  • H03H17/02—Frequency selective networks
  • H03H17/0294—Variable filters; Programmable filters
• • H—ELECTRICITY
  • H03—ELECTRONIC CIRCUITRY
  • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
  • H03H11/00—Networks using active elements
  • H03H11/02—Multiple-port networks
  • H03H11/04—Frequency selective two-port networks
  • H03H11/0422—Frequency selective two-port networks using transconductance amplifiers, e.g. gmC filters
  • H03H11/0472—Current or voltage controlled filters
• • H—ELECTRICITY
  • H03—ELECTRONIC CIRCUITRY
  • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
  • H03H11/00—Networks using active elements
  • H03H11/02—Multiple-port networks
  • H03H11/04—Frequency selective two-port networks
  • H03H11/0422—Frequency selective two-port networks using transconductance amplifiers, e.g. gmC filters
  • H03H11/0433—Two integrator loop filters
• • H—ELECTRICITY
  • H03—ELECTRONIC CIRCUITRY
  • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
  • H03H11/00—Networks using active elements
  • H03H11/02—Multiple-port networks
  • H03H11/04—Frequency selective two-port networks
  • H03H11/0422—Frequency selective two-port networks using transconductance amplifiers, e.g. gmC filters
  • H03H11/0455—Multiple integrator loop feedback filters
• • H—ELECTRICITY
  • H03—ELECTRONIC CIRCUITRY
  • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
  • H03H11/00—Networks using active elements
  • H03H11/02—Multiple-port networks
  • H03H11/04—Frequency selective two-port networks
  • H03H11/12—Frequency selective two-port networks using amplifiers with feedback
  • H03H11/1217—Frequency selective two-port networks using amplifiers with feedback using a plurality of operational amplifiers
  • H03H11/1252—Two integrator-loop-filters
• • H—ELECTRICITY
  • H03—ELECTRONIC CIRCUITRY
  • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
  • H03H11/00—Networks using active elements
  • H03H11/02—Multiple-port networks
  • H03H11/04—Frequency selective two-port networks
  • H03H11/12—Frequency selective two-port networks using amplifiers with feedback
  • H03H11/1291—Current or voltage controlled filters
• • H—ELECTRICITY
  • H03—ELECTRONIC CIRCUITRY
  • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
  • H03H17/00—Networks using digital techniques
  • H03H17/02—Frequency selective networks
  • H03H17/0248—Filters characterised by a particular frequency response or filtering method
• • H—ELECTRICITY
  • H03—ELECTRONIC CIRCUITRY
  • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
  • H03H2210/00—Indexing scheme relating to details of tunable filters
  • H03H2210/01—Tuned parameter of filter characteristics
• • H—ELECTRICITY
  • H03—ELECTRONIC CIRCUITRY
  • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
  • H03H2210/00—Indexing scheme relating to details of tunable filters
  • H03H2210/01—Tuned parameter of filter characteristics
  • H03H2210/012—Centre frequency; Cut-off frequency

Definitions

• Analog logic in turn, has its own limitations. Because analog circuits are not formed of truly independent blocks, changing one block of analog logic can force changes in every other block in the circuit. In addition, advances in process technology occur so quickly that application-specific designs often become obsolete before they are fabricated. Finally, analog circuits are neither fully reconfigurable nor fully programmable.
• Embodiments of the present invention include methods of tuning state variable filters. Examples include state variable filters whose center frequencies can be tuned using variable gain blocks coupled to outputs of filter integrators. First- and second-order state variable filters may operate on signals in parallel and their outputs combined to produce a filtered output. Filters may be tuned to pass or reject signals depending on the application; sample applications include, but are not limited to: agile filtering; spectrum analysis; interference detection and rejection; equalization; direct intermediate-frequency transmission; and single- sideband modulation and demodulation.
• a method of tuning a filter of a biquad circuit includes tuning a loss pad to generate a target gain value at a predetermined frequency.
• a phase of a first integrator is tuned to a target phase at the predetermined frequency.
• a phase of a second integrator is then tuned to the target phase at the predetermined frequency.
• a gain of the first integrator is tuned to a target gain value at the predetermined frequency.
• a gain of the second integrator is tuned to the target gain value at the predetermined frequency.
• the target gain at the predetermined frequency is determined.
• Tuning the loss pad may include adjusting an attenuation value at the loss pad.
• Tuning the phase of the first integrator may include adjusting a phase value of an input at the first integrator, the phase value controlling the phase of the first integrator.
• Tuning the gain of the first integrator may include adjusting a coarse gain value and adjusting a fine gain value at the first integrator, the coarse gain value and fine gain value controlling the gain of the first integrator.
• Tuning the phase of the second integrator may include adjusting a phase value of an input at the second integrator, the phase value controlling the phase of the second integrator.
• Tuning the gain of the second integrator may include adjusting a coarse gain value and adjusting a fine gain value at the second integrator, the course gain value and fine gain value controlling the gain of the second integrator.
• FIG. 1 is a block diagram of a first-order state variable filter.
• FIG. 2A is a block diagram of a control canonical form of a second- order state variable filter.
• FIG. 2B is a block diagram of a configuration of biquad circuits in which embodiments of the invention may be implemented.
• FIG. 3 is a block diagram of am observer canonical form of a second-order state variable filter.
• FIG. 4 is flow diagram that illustrates signal filtering according to principles of the present invention.
• FIG. 5A is a block diagram of a signal interface at a state variable filter.
• FIG. 5B is a block diagram of serial peripheral interface (SPI) data assignment for a state variable filter.
• SPI serial peripheral interface
• FIG. 5C is a block diagram illustrating test point connections to measure operation of the state variable filter.
• FIG. 6 is a state diagram of a process of tuning a state variable filter.
• FIG. 7 is a flow diagram of a process of tuning a loss pad.
• FIG. 8 is a flow diagram of a process of tuning an integrator phase.
• FIG. 9 is a flow diagram of a process of tuning a phase of an additional integrator.
• FIG. 10 is a flow diagram of a process of tuning an integrator gain.
• FIG. 11 is a flow diagram of a process of tuning a gain of an additional integrator.
• FIGs. 12A-B are graphs illustrating a result of controlling an integrator.
• FIG. 13 is a circuit diagram of a circuit for tuning integrator gain.
• FIGs. 14A-B are charts illustrating an example coarse tuning of an integrator.
• FIGs. 15A-B are circuit and flow diagrams illustrating an example tuning of a state variable filter for operation as a notch filter.
• FIG. 16A-B are circuit and flow diagrams illustrating an example tuning of a state variable filter for operation as an all-pass (delay) filter.
• Wideband and ultrawideband (UWB) communication systems which spread signal energy finely across an enormous frequency band (e.g., 3.7-10.0 GHz), appear promising for many wireless applications.
• RFID radio-frequency identification
• wideband systems that operate at baseband do not require down-conversion at the receiver, simplifying the required receiver.
• Analog-to-digital (A/D) conversion limits the bandwidth and dynamic range (resolution) of all-digital receivers.
• the high-fidelity A/D converters capable of adequately sampling baseband UWB signals are too complex and consume too much power, particularly for RFID applications.
• Alternative all-digital systems rely on low-resolution A/D converters, but do not perform as well.
• analog correlators as the bandwidth grows, the number of rake fingers for efficient energy capture increases, and, thus, so does the circuit complexity and difficulty of channel estimation.
• transmitted reference receivers are attractive for low-to-moderate data rate operations, they require large-bandwidth delay lines at the receiver for UWB applications.
• WiSP wideband signal processing
• Embodiments of the disclosed invention employ a state variable-based architecture to implement any desired impulse response or transfer function to a specifiable degree of accuracy. All filter parameters, including center frequency, can be controlled and optimized through algorithms running on a low data rate, wideband digital signal processor (DSP) or other suitable control element running in the control path. Wideband signal processors can be implemented on sub-micron complementary metal-oxide-semiconductor (CMOS) structures to permits processing of broadband signals, including signals whose bandwidths exceed 10 GHz.
• CMOS complementary metal-oxide-semiconductor
• Embodiments of the disclosed WiSP systems and devices include dynamically and reconfigurable filters that can be used as or in: wideband filters; agile filters; adaptive filters; equalizers; direct intermediate-frequency (IF) transmitters; and single-sideband modulators and demodulators.
• Filters, processors, equalizers, and tapped delay lines made according to principles of the present invention can be used in a wide variety of applications, including, but not limited to: active RFID; radar; imaging; software-defined radio;
• coefficients of the filter are controlled by the C-plane.
• DSPs Digital Signal Processing
• the underlying mathematical basis for digital signal processing is based on S-plane theory, synchronous sampling at or above the Nyquist sampling rate— governed by the sampling theorem. Needless to say, systems implementing such functionality rely on the use of DSP, A/D, and digital-to-analog (D/A) technologies.
• the S-plane undergoes sophisticated analog signal processing (the signal path is all analog) while maintaining 10+ GHz of bandwidth.
• the C-plane is implemented in a traditional A/D, D/A, and DSP architecture.
• Embodiments disclosed herein have extremely low power consumption relative to today's standards because of the resulting low gate count and block-architecture of these hybrid systems.
• Filters are building-block components for analog signal processors that alter the amplitude and/or phase characteristics of a signal with respect to frequency, making it possible to process signals in the S-plane. Filters are used to pass signals within certain frequency ranges and to reject those in other ranges. Bandpass filters transmit only those frequencies that fall within a given band. Notch or band-reject filters, on the other hand, remove specific frequencies while allowing all other frequencies to pass undisturbed. Low-pass and high-pass filters reject frequencies above and below, respectively, a cut-off frequency. All-pass filters impart phase shifts on an input signal without attenuating the signal.
• a filter's frequency response can be represented mathematically by a transfer function, which is the ratio of the Laplace Transforms of its output and input signals.
• Ideal filters have rectangular transfer functions; that is, transfer functions with infinitely steep boundaries between the pass and stop bands, and a constant gain in the pass band.
• ideal filters have linear phase responses to avoid introducing phase distortion into the signal. Real filters can only approximate the ideal response.
• the order of a filter equals the order of the polynomial expansion of the filter's transfer function.
• higher-order filters are constructed by cascading (i.e., serially connecting) lower-order filters.
• a third-order filter can be constructed by connecting the output of a first-order filter to the input of a second-order filter.
• Higher-order filters typically have improved pass band performance and a faster roll-off
• complex pole/residue pairs occur as complex conjugate pairs and can be combined as: R, R,
• Fig. 1 shows a first-order state variable filter 100 used to implement real solutions to equations (2) and (3).
• the first-order state variable filter 100 operates on a wideband input u(t) to produce a filtered output ⁇ ⁇ (t) .
• a residue block 140 determines the input's residue R f , which is forwarded to a summer
• the first-order state variable filter 100 includes a variable gain block 130 that operates on the output of the integrator 120.
• the variable gain block 130 amplifies or attenuates the integrated signal according to its gain settings G to produce the filtered output.
• a pole block 150 coupled to the variable gain block 130 produces the pole p i of the filtered output, which is fed back to the summer 1 10.
• Changing the parameters of the pole block 150 and the residue block 140 i.e., changing the filter tap weights) changes the filter transfer characteristics, including the filter center frequency and pass bandwidth.
• variable gain block 130 acts as a frequency scale when preceded by the integrator 120 (which is equivalent to ⁇ l s in the Laplace domain).
• the variable gain block 130 transforms the filter transfer function T(s) into T(s/G) , where G is the gain of the variable gain block 130.
• Varying G causes the center frequency of the filter passband to tune across the UWB band.
• Fig. 2 A and 3 show second-order state variable filters 200 and 300 in control and observer canonical forms, respectively, that realize second-order solutions to equations (2) and (3).
• the two forms are mathematically equivalent, but the observer form 300 requires an additional summer and has differently configured inputs and outputs.
• the second-order filters 200 and 300 include variable gain blocks that change the center frequency of the filter passband. They also include tap weights, or fractional gain blocks, that represent coefficients (i.e., «0, a ⁇ , a 2 , bo, b ⁇ , and 6 2 ) o the transfer function in equation (4).
• the fractional gain blocks attenuate or amplify signals according to a corresponding coefficient.
• the variable and fractional gain blocks scale signals to a value within a normalized range of -1 to 1, inclusive.
• the control second-order state variable filter 200 shown in Fig. 2 operates on a wideband input u ⁇ t) to produce a filtered output x 2 (t) .
• a summer 210 combines the wideband input with outputs from fractional gain blocks 240 and 241.
• the summer 210 passes the difference of the wideband input and the fractional gain block outputs to a third fractional gain block 242, which scales the summer output by an amount l/ ⁇ 3 ⁇ 4.
• the fractional gain block 242 forwards the scaled summer output to an integrator 220 and a fractional gain block 252, which scales the scaled summer output by Z> 2 .
• the integrator 220 integrates the scaled signal, then forwards a resulting integrated signal to a variable gain block 230, which tunes the passed signal frequency according to its gain setting G ⁇ .
• the output of the variable gain block 230 is forwarded to a second integrator 221 and fractional gain blocks 241 and 251, which scale the output by a ⁇ and respectively.
• the second integrator 221 integrates the signal again, then forwards a resulting second integrated signal to a variable gain block 231.
• the output of the variable gain block 231 is forwarded to fractional gain blocks 240 and 250, which scale the output by 0 and bo, respectively.
• a summer 21 1 combines the outputs of the fractional gain blocks 250-252 to provide the filtered output.
• Fig. 2B illustrates a series of state variable filter circuits (also referred to as "biquad circuits"), such as the filter 200 described above in Fig. 2A.
• the biquad configuration is a second order state variable structure.
• IN ⁇ order transfer function T(sy is obtained by cascading N biquads.
• Fig. 2B also describe a single input single output (SISO) field programmable analog array (FPAA).
• SISO single input single output
• FPAA field programmable analog array
• the observer second-order state variable filter 300 shown in Fig. 3 operates on a wideband input u t) to produce a filtered output x 2 (t) in much the same way as the filter 200 shown in Fig. 2.
• fractional gain blocks 350, 351 , and 352 scale the wideband input by amounts bo, b ⁇ , and & 2s respectively, and forward the resulting scaled outputs to summers 310, 31 1 , and 312, respectively.
• the summer 310 combines (subtracts) a scaled output from fractional gain block 340 with (from) the output of fractional gain block 350 to provide a combined signal.
• An integrator 320 integrates the resulting signal, then forwards a resulting integrated signal to a variable gain block 330, which tunes the passed signal frequency according to its gain setting.
• a second summer 31 1 combines the output of the variable gain block 330 with outputs from fractional gain blocks 341 and 351 to provide a second combined output.
• a second integrator 321 integrates the second combined output, then forwards a resulting second integrated signal to a second variable gain block 331.
• a third summer 312 combines the second variable gain block's output with the output of the fractional gain block 352 to provide a third combined signal.
• a fractional gain block 342 scales the third combined signal by l/ ⁇ 3 ⁇ 4 to provide the filtered output.
• the filtered output is forwarded to fractional gain blocks 340 and 341 , which scale the filtered output by a 0 and a ⁇ , respectively.
• the first- and second-order state variable filters shown in Figs. 1-3 can be generalized to any order by incorporating or removing additional integrators and variable gain blocks as appropriate.
• An nth-order state variable filter can be constructed by coupling a variable gain block to the respective outputs of each of n integrators.
• Higher-order state variable filters may also include additional functional gain blocks and summers configured to scale and combine signals at various points throughout the filter. Setting a functional gain block's scaling coefficient to 0 or 1 (depending on the filter configuration) effectively suppresses the functional gain block's effect on the filter's operation.
• a series of multiple biquad circuits may be connected in series, as described above with reference to Fig. 2B, to obtain a 2 ⁇ order transfer function T(sy by cascading N biquad circuits.
• FIG. 4 is a flow diagram that illustrates basic signal filtering 400 according to principles of the present invention.
• a wideband input 402 is combined (404) with a pole 418 to produce a combined signal 406, where the pole 418 is determined from a filtered signal 416 derived through the signal filtering 400.
• the pole 418 may be derived by scaling the filtered signal 416 with a fractional gain coefficient.
• the combined signal 406 is integrated (408) to produce an integrated signal 410, which is amplified (412) by a variable gain 414 to produce the filtered signal 416. Changing the variable gain 414 shifts the center frequency of the filtered signal 416.
• Example embodiments of the present invention provide methods for tuning a state variable filter (also referred to herein as a "biquad filter”) such as those described above with reference to Figs. 1-4.
• a state variable filter also referred to herein as a "biquad filter”
• Embodiments of wideband filters usable with the present invention are described in further detail in "Method, System, and Apparatus for Wideband Signal Processing," (U.S.
• a tuning procedure may be performed in order to increase the filter's performance in a number of ways, such as by compensating for potential inaccuracies inherent in its implementation as an integrated circuit. As a result of the tuning procedure, a greater degree of precision is created than would otherwise be achievable.
• FIG. 5A is a block diagram of a signal interface at a state variable filter, illustrating both data signal and control planes.
• the interface may be implemented with a state variable filter such as those described above with reference to Figs. 1-4.
• the control plane interacts with the signal plane in order to tune the filter, and thereby the biquad's cascaded constructions that implement biquad filters.
• the control plane may operate at a lower frequency than the biquad's operating range (e.g., 100 MHz) and provides a measurement mechanism that improves the biquad's performance by accurately setting the gain and phase of its sub-components (such as loss pads and integrators).
• Measurements are output from the control plane to an ADC and are used to change circuit values within the biquad to improve accuracy.
• a serial peripheral interface (SPI) interface is used to read and write values within the biquad.
• the biquad's SPIs may be treated as slaves to a microprocessor/digital signal processor ( ⁇ /DSP) master.
• ⁇ /DSP microprocessor/digital signal processor
• SPI addresses are distributed within the biquad in order to change circuit values. Taking an 8 th order bandpass filter as an example, there are:
• Figs. 5B-C are block diagrams illustrating data and test point connections at an example biquad circuit. The connections are utilized in the example tuning procedures described below with reference to Figs. 6-16B.
• Fig. 5B illustrates an example SPI Data Assignment for the biquad
• Fig. 5C illustrates test point connections to measure operation of the biquad.
• An example registry and address configuration for the data and test point connections of Figs. 5B-C is provided in Tables 1-5, below.
• Table 2 SPI Data Assignment for Biquad (Address Bits from LSB 0 to MSB 24)
• Vcip BQ2 Low Injects 100 MHz source into biquad from control
• Vctpl BQ3 Low Selects Test Point 1 in each biquad
• Vctp2 BQ3 Low Selects Test Point 2 in each biquad
• Vctp3 BQ3 Low Selects Test Point 3 in each biquad
• Vctp4 BQ3 Low Selects Test Point 4 in each biquad
• An example SPI connected to tune a biquad circuit may operate at a frequency of 40 MHz. Using a serial rapid I/O interface, the control plane can operate at speeds up to 20 Gbps. 32-bit words (7-bit address and 25-bit data registers) may be used to provision integrators and loss pads. An example 8 th order bandpass filter may be made up of four biquads connected in series, where each biquad includes two integrators and one loss pad. Overall provisioning time is dependent on the details of the provisioning and tuning procedure.
• a) Design a desired transfer function using classical techniques. Taking a bandpass filter as an example, determine filter type, order, center frequency, bandwidth, and passband ripple.
• mapping maps these to the transfer function implemented by the biquad filter circuit.
• the mapping can be of the form:
• Fig. 6 is a state diagram of a process of tuning a biquad circuit for configuration as an example 8 th order bandpass filter. This procedure may be carried out successively for each of the 4 biquads connected in series, which comprise the filter. A similar procedure, in which biquad subcomponents such as loss pads and integrators are tuned for phase, and/or gain precision, performed for other filters. The procedure may be as follows:
• steps 7-11 i.e., tuning the loss pad and the phase/gain of integrators 1 and 2
• steps 7-11 i.e., tuning the loss pad and the phase/gain of integrators 1 and 2
• Fig. 7 is a flow diagram of a process of tuning a loss pad as in the filter tuning procedure of Fig. 6. Tune the loss pad controlling a ! as follows:
• Fig. 8 is a flow diagram of a process of tuning the phase of integrator 2 as in the filter tuning procedure of Fig. 6. Tune Integrator 2 Phase as follows:
• BMlInt2_Phase_Indicator_IN BM2Int2_Phase_Indicator_IN, respectively.
• Int2_Phase__IndicatorIN by adjusting BMl and BM2 using MTR6 ⁇ 12:23> and MTR6 ⁇ 0: 1 1>. Then record the detector output (from Multiplier) through ADC read and BM l and BM2 meter attenuations as Int2_Phase_IndicatorIN,
• the VCR2 adjustment follows a gradient search algorithm which adjusts step size in proportion to the gradient's deviation from its expected value (expected value range is TBD). Example: 3-5 LSBs for large deviation, 1 LSB for small one. Repeat process from step (1).
• Fig. 9 is a flow diagram of a process of tuning a phase of integrator 1 as in the filter tuning procedure of Fig. 6.
• BMlIntl_Phase_Indicator_OUT and BM2Intl_Phase_Indicator_OUT, respectively.
• Reset Attenuator by setting BM1 &BM2 to zero attenuation (all 0's) using MTR6 ⁇ 12:23> and MTR6 ⁇ 0:11>.
• BM 1 Intl Phase JndicatorJN and BM2Int 1 _Phase_Indicator_IN , respectively.
• Intl_Phase_IndicatorIN by adjusting BM1 and BM2 using MTR6 ⁇ 12:23> and MTR6 ⁇ 0: 1 1>. Then record the detector output (from Multiplier) through ADC read and BM1 and BM2 meter attenuations as Intl_Phase_IndicatorrN,
• BMlIntl_Phase_Indicator_IN and BM2Intl_Phase_Indicator_rN, respectively. Decrease SRC Attenuator Settings to Increase Signal Level [MTR7 ⁇ 0: 11>]. Return to (1).
• Fig. 10 is a flow diagram of a process of tuning the gain of integrator 2 as in the filter tuning procedure of Fig. 6.
• Integrator 2 Gain Tuning Initialization Ensure all integrator switch settings are the same initial value. Initial value based on wrn, which falls into 1 of 7 coarse frequency bins. For example, 5th bin is 101 for Vil_sw and Vi2_sw using BQn_2 ⁇ 12: 14> and BQn_3 ⁇ 0:2>, respectively. Set VCC2 to initial value (-900 mV) using BQn_5 ⁇ 12:23>.
• Fig. 11 is a flow diagram of a process of tuning a gain of integrator 1 as in the filter tuning procedure of Fig. 6. Tune Integrator 1 Gain as follows:
• Integrator 1 Gain Tuning Initialization Ensure all integrator switch settings are the same initial value. (Initial value based on wrn, which falls into 1 of 7 coarse frequency bins. For example, 5th bin is 101 for Vil sw and Vi2_sw using BQn_2 ⁇ 12: 14> and BQn_3 ⁇ 0:2>, respectively. Set VCC1 to initial value ( ⁇ 900 mV) using BQn_2 ⁇ 0: l 1>.
• Figs. 12A-B are grans illustrating integrator control
• VCR1 , VCR2 , VCapA, Vil_sw, Vi2_sw, VCC1, VCC2 are the primary pins involved in integrator phase and gain tuning.
• VCapA (its inclusion depends on operating frequency) are set first to tune the phase response to -89° target phase shift.
• Vil_sw, Vi2_sw, VCC1, and VCC2 are set second to tune the gain to the target value.
• Their associated bits control the phase and gain values.
• Fig. 13 is a circuit diagram of a circuit for tuning integrator gain.
• inputs Vi l sw / Vi2_sw connect to switches at left to control coarse gain tuning, and inputs VCC1 / VCC2 control fine gain tuning through CL.
• a chart illustrating example course tuning values is shown in Figs. 14A-B.
• assignment of inputs to control the loss pad, as well as phase and gain of the integrators may be as follows:
• Pin VCapA controls fine phase adjustment of Integrators 1 and 2, if required. Its 12 associated bits control the phase value. Its use is dependent on the operating frequency range and is only required for frequencies of operation that exceed a given threshold (for example, 1.5 GHz).
• Vca_l controls attenuation adjustment of the Loss Pad controlling al . Its 12 associated bits control the loss value.
• FIGs. 15A-B are circuit and flow diagrams illustrating an example tuning of a state variable filter for operation as a notch filter.
• Fig. 15A illustrates a computation of a transfer function to be realized via the tuning procedure.
• the state diagram of Fig. 15B follows an empirically-determined procedure to tune the state variable filter for operation as a notch filter. After building a bandpass filter as through the state machine of Fig. 6, 'b' coefficients are adjusted. The bl loss pad is changed to "Max Attenuation" while bO and b2 are adjusted from maximum attenuation to "No Attenuation". If these adjustments fail to create the desired notch filer, further refinement of the bO loss pad gain and phase and b2 loss pad gain can be performed.
• FIG. 16A-B are circuit and state diagrams illustrating an example tuning of a state variable filter for operation as an all-pass (delay) filter.
• Fig. 15 A illustrates a computation of a transfer function to be realized via the tuning procedure.
• the state diagram of Fig. 15B follows an empirically-determined procedure to tune the state variable filter for operation as an all-pass (delay) filter. After building a bandpass filter as in the state machine of Fig. 6, 'b' coefficients are adjusted.
• the bl loss pad is set to the al loss pad value and the bl switch goes from positive to negative.
• the bO and b2 loss pads are adjusted from maximum attenuation to "no attenuation.” If these changes do not create the desired all-pass filter, further refinement of the bO loss pad gain and phase and b2 loss pad gain can be performed.

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