Calculating Maximum Processing Rates of the
PDC (HSP50214, HSP50214A and HSP50214B)
®
Application Note
Introduction
January 1999
AN9720.2
BAND OF INTEREST
Configuring the Programmable Digital Downconverter (PDC)
requires selecting clock, decimation and interpolation rates for
the various filter sections. Each filter section has limitations due
to the hardware implementation. Furthermore, the input and
output rates of the various sections must match in order for the
composite configuration to be valid. In many cases, there may
be multiple configurations that will yield the desired composite
conversion and filter. In a few applications, a particular
hardware constraint or specification will drive the complete
configuration. This application note reviews the application of
system requirements to the PDC, details the hardware
constraints, introduces design approaches to the PDC, and
then details the hardware constraints; section by section.
The input sample rate, CLKIN, is 52MHz, for the original part
and 65MHz for the A and B mask revisions. The PROCCLK
rate is 35MHz on the original part and 55MHz for the A and B
mask revisions. Calculations for the A and B versions will be
given in brackets following the calculation for the original part.
REFCLK is a local reference input that can be used to phase
lock the PDC output sample rate to local clocks. External clock
recovery loop filters are required to process the PDC “Timing
Error” into a valid Resampler NCO control input. Since the rates
of the PDC output and the local clocks can be different, refer to
the Polyphase Filters and Interpolating Halfband Filters section
for guidance in selecting the NCO and REFCLK frequencies.
Mapping System Constraints into PDC
Configuration
Three system parameters that will drive the PDC
configuration are: 1) IF frequency, 2) the Bandwidth of
Interest, and 3) the baud rate of the baseband data. This
section details the first pass design configuration of the PDC
based on these three system parameters. Once this first
pass is completed, the remaining information in this
application note will be used to optimize the PDC design
configuration.
System Input Specifications
The IF frequency and the Bandwidth of Interest are used to set
the minimum input sampling frequency, fS , of the PDC.
Considerations are: 1) A/D Full Power Input Bandwidth, 2) the
maximum clock rate of the A/D converter, and 3) the 52MHz
maximum PDC input sampling rate. If the IF frequency is in the
upper portion of the A/D bandwidth and that bandwidth is
greater than the maximum sample rate of the A/D or PDC, then
use of undersampling techniques to process a lower frequency
sampling alias of the IF signal should be considered. This is
illustrated in Figure 1.
1
INPUT SPECTRUM
A/D
BANDWIDTH
INPUT SPECTRUM & A/D BANDWIDTH
(N-1)FS
SAMPLED INPUT SPECTRUM
(N-1)FS
(N)FS
ANTI-ALIASING FILTER
(N)FS
SAMPLED SPECTRUM SHOWING ANTI-ALIAS FILTER
DC
FS
SAMPLED SPECTRUM
FIGURE 1. CONSIDERING IF FREQUENCY, A/D
BANDWIDTH, AND ALIASING IN SELECTION
UNDERSAMPLING
If the IF is in the lower portion of the A/D bandwidth and is
below the maximum rate of the A/D and the PDC, then
traditional oversampling techniques should be considered.
This is illustrated in Figure 2. In both cases, consideration of
signals outside the band of interest, but inside the A/D
converter bandwidth must be considered to avoid alias
interference or reduction of dynamic range. The design of
the IF alias filter (bandwidth, rolloff, rejection and cost) will
be an important part of this consideration. It is likely that
selecting the input sampling rate to meet the Nyquist rate for
the bandwidth of interest and the spectral purity
requirements, will involve reviewing several frequency plans
with a variety of sampling frequencies.
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Application Note 9720
With the FIR, halfband filter, and CIC rates set, two checks
must be performed to validate this first pass PDC
configuration: 1) the composite dynamic range - set primarily
in the CIC and Halfbands, and 2) the number of clocks
required for filter calculation must be met. Information
provided in the detailed filter sections will provide the
parameters needed to complete these checks.
BAND OF INTEREST
A/D
BANDWIDTH
INPUT SPECTRUM AND A/D BANDWIDTH
Hardware Constraint Overview
DC
fS
SAMPLED INPUT SPECTRUM
FIGURE 2. CONSIDERING IF FREQUENCY, A/D
BANDWIDTH, AND ALIASING IN SELECTION
Hardware Constraint Overview
System Output Specifications
The system output specifications that affect the configuration
of the PDC are the baseband baud rate and/or baseband
bandwidth. The baud rate or equivalent low pass bandwidth
sets the PDC output sample rate or the minimal PDC
bandwidth. In some digital systems the baseband output rate
is required to be a submultiple of the A/D converter sample
rate. The relationship between input and output sampling rate,
or total decimation is fixed and must be distributed among the
various filter elements while creating a composite filter
meeting the low pass bandwidth and the PDC hardware
constraints. The detailed section of this document will provide
the possible decimation rates for each filter section.
The 255 tap FIR filter input sampling rate should be set at
greater than or equal to twice the lowpass bandwidth, since this
is the narrowest filter section in the PDC. If use of even one
stage from the Halfband filter is required, then the 255 tap FIR
filter input sampling rate should be set at greater than or equal
to four times the lowpass bandwidth, to minimize the alias
effects on dynamic range. Setting the 255 tap FIR filter input
rate sets the number of PROCCLKS available for filter
calculations, and thus determines the number of filter taps
possible.
The Halfband filter input sample rate is set at 2N times the
FIR input sample rate, where N is the number of halfband
filter stages active. Note that each halfband stage will
decimate by 2.
The CIC filter input is sampled at fS , so it must provide a
decimation of fS /FHBIN. The CIC filter also affects the
dynamic range. At a bandwidth of 1/8 the CIC output sample
rate, the CIC filter provides 84dB of dynamic range. At a
bandwidth of 1/10 the CIC output sample rate, the CIC filter
provides 96dB of dynamic range. At a bandwidth of 1/12 the
CIC output sample rate, the CIC filter provides 100dB of
dynamic range.
2
This section provides an outline overview of the clocking and
timing constraints of each major functional block in the PDC.
More details on these constraints can be found in the
respective section of this application note, or in the
HSP50214 Data Sheet [1]. The intention of this outline
overview is to introduce the reader to timing issues that
should be kept in mind as the detailed sections of the PDC
data sheet and this application note are studied.
1. Summary of Rate and Bandwidth Constraints
The PDC contains a set of very flexible filter blocks. Each
filter set offers a unique design feature. The CIC offers a
broad passband and initial broad stopband capability. The
Halfband offers sample rate reduction and bandwidth
reduction in multiples of 2. The 255 tap FIR offers high
resolution filter response shaping and contouring. The
Polyphase Re-Sampling FIR offers non-integer rate
changes. The Interpolation HalfBand filters offer
oversampling. The discriminator FIR offers bandwidth
reduction. Figure 3 summarizes the rate changes (in terms
of decimation) and bandwidth adjustments that occur in the
various filter blocks of the PDC.
DECIMATION
BANDWIDTH
4 TO 32
1/8 fS
(84dB DYNAMIC
RANGE BW)
2N
(0 ≤ N ≤ 5)
1/2(2+N) fS
(ALIAS FREE)
255 TAP FIR
FILTER
1 TO 16
BY DESIGN
(1/4 fS FOR GOOD
DYNAMIC RANGE)
Resampler
POLYPHASE FIR
FILTER
1 TO 4
(NON-INTEGER
VALUES OK)
1/4 fS
INTERPOLATING
HALFBAND
FILTERS
1/2 OR 1/4
2 OR 4 fS
FREQUENCY
DISC. FIR
FILTER
1 TO 8
BY DESIGN
CIC
FILTER
HALFBAND
FILTERS
NOTE: fS = INPUT SAMPLE RATE OF THE FILTER BLOCK
FIGURE 3. OVERVIEW OF RATES AND BANDWIDTHS
Application Note 9720
2. CIC Filter
CLKIN.
≤52MHz [≤65MHz]
b) Compute Clock:
CLKIN.
≤52MHz [≤65MHz]
c) Decimation Range:
4 to 32.
a) Input Sample Rate:
The HB filter input sample rate is required to be less than
PROCCLK by an amount determined by the number of
halfband filters selected. The range of the divisor is 3 to 9.75
(See Table 8 and 8A in the HB Filter Section). NOTE: If the
Halfband is bypassed, decimation may be required in the 255
d) Filter Characteristics See Table 1
TABLE 1. CIC FILTER CHARACTERISTICS
tap FIR filter to lower the sample rate to the PROCCLK/6
requirement of the AGC.
FREQUENCY
(fCIC_Out/)
PASSBAND
ATTENUATION (dB)
ALIAS
ATTENUATION (dB)
/4
4.6
52
/5
2.9
63
b) Compute Clock:
PROCCLK
/6
2.0
72
c) Decimation:
1 to 16.
/8
1.1
85
/10
0.72
96
d) The maximum number of taps is 255 for a symmetric filter, 128
for an asymmetric filter, and 64 for a complex filter.
/12
0.50
105
a) Input Sample Rate:
If the CIC is bypassed, the sync circuitry requires that the ENI signal
drop low, then go high to pass data from the CIC input to the output.
For wide output bandwidths, some emphasis of the higher frequencies in the programmable FIR may be needed to flatten the
passband.
3. Halfband Filters
a) Input Sample Rate:
Equal to the output sample rate of the
CIC Filter Section.
b) Compute Clock:
PROCCLK. ≤35MHz [≤55MHz]
c) Number of Stages:
0 to 5.
d) Decimation:
2 Number of stages,
(each stage decimates by 2).
Equal to the output rate of the halfband filter block.
≤35MHz [≤55MHz].
e) The number of taps available depends on the processing
clock, the input sample rate, and the symmetry of the filter.
See Table 3.
TABLE 3. DETERMINING THE NUMBER OF FILTER TAPS
FILTER TYPE
EQUATION FOR NUMBER OF
FILTER TAPS
Real, Symmetric, Even # Taps [PROCCLKS/fSAMP/R) -R]*2
Real, Symmetric, Odd # Taps
[{PROCCLKS/fSAMP/R) -R} -1]*2
Real, Asymmetric
[PROCCLKS/(fSAMP/R) -R]
Complex
[PROCCLKS/fSAMP/R) -R]/2
Where CLKS = PROCCLK divided by the output sample rate
of the FIR (quotient truncated to nearest integer) and R is
the decimation factor.
e) Filter Characteristics:
f) Each coefficient bits has 22 bits.
i) Halfband filters have very flat passband responses.
ii) The passband attenuation of each filter stage is -6dB at 1/4
the input sample rate for the stage (i.e., the attenuation is
-6dB at the folding frequency of the output spectrum).
iii) Filter characteristics - alias attenuation: See Table 2
TABLE 2. CIC FILTER ALIAS ATTENUATION
fOUT /2
fOUT /4
fOUT /8
fOUT /16
HB5
6dB
105dB
102dB
110dB
>110dB
103dB
HB4
6
50
>110
>110
>110
>110
HB3
6
40
88
>110
>110
>110
HB2
6
32
66
104
>110
>110
HB1
6
25
48
72
98
>110
fOUT /32 fOUT /64
f) When all five halfbands are enabled, the alias attenuation for
the filters align as follows: f OUT HB1/64 = f OUT HB2/32 =
f OUT HB3/16 = f OUT HB4/8 = f OUT HB5/4.
g) The filter computation requirements (per input sample): HB5
requires 7 clocks; HB4 requires 6 clocks; HB3 requires 5
clocks; HB2 requires 4 clocks; HB1 requires 3 clocks.
h) When cascading filters, the computational requirements are:
[(clocks for last filter) + 2 * (clocks for second to last filter) + 4
* (clocks for third to last filter) + ...]/2∧ (number of filters -1)).
For example, using HB5, HB4, and HB3, the number of processing clock (PROCCLK) cycles needed per input sample to
the Halfband Filter Section is: (7 + 2*6 + 4*5)/(2∧ (3 -1) = 9.75.
3
4. 255 Tap FIR
Filter bypass is achieved by setting the center tap to 1 and
taps C-1 and C1 to zero. A rule of thumb for the largest
number of taps that can be achieved is:
(PROCCLK)/ ( f FIROUT )-R) x 2 Number of Taps
(EQ. 1)
5. AGC
a) Input Sample Rate:
Equal to the output sample rate of the
programmable FIR.
b) Compute Clock:
PROCCLK
c) Decimation:
None.
≤35MHz [≤55MHz].
d) The processing clock must be at least 6 times the input sample rate of the AGC.
The AGC requires 6 PROCCLKS to process data - always.
The AGC functional bypass can be effected by setting the
upper and lower AGC limits to an identical number. The
bypass mode still requires 6 PROCCLKS to complete the
calculation.
6. Resampler Filter and Interpolating Halfband Filters
a) Input Sample Rate:
Equal to the output sample rate of the
programmable FIR PROCCLK.
b) Compute Clock:
PROCCLK
c) Decimation:
1 to 4, NCO controlled, non-integer al-
≤35MHz [≤55MHz].
Application Note 9720
7. Cartesian to Polar Coordinate Converter
lowed.
d) The coefficients are fixed.
e) The output sample rate is controlled by the Resampler NCO.
The Resampler NCO is 32 bits and is updated at the Resampler input sample rate. The output frequency is: fIN * N/232,
where fIN is the input sample rate for the block, N is the 32-bit
control word (unsigned, 0 to 2, 0 to 232-1).
f) The spacing between output samples varies between 1/fIN
and 2/fIN.
g) The resampling process produces a higher noise floor than
the other filters due to the filter response and the aliasing of
the filtered interpolation images.
h) Filter characteristics: See Table 4.
TABLE 4. RESAMPLER FILTER CHARACTERISTICS
FREQUENCY (*fIN)
AMPLITUDE (dB)
0
0
0.125
-0.24
0.25
0
0.375
-2.6
0.5
-9.6
0.625
-24.2
0.75
-67.6
0.875
-62.4
i) The bandwidth of the signal into the Resampler should be less
than fIN /4 to minimize aliasing.
j) All band selection filtering should be done before the Resampler.
k) The Resampler and Interpolation Halfband filter use the same
compute engine. The number of processing clocks per input
sample required for the possible filter configurations are
shown in Table 5.
TABLE 5. PROCESSING CLOCK REQUIREMENTS FOR THE
RESAMPLER AND INTERPOLATING HALFBAND
FILTERS
CONFIGURATION
PROCESSING CLOCK
CYCLES PER INPUT SAMPLE
Resampler
6
Resampler + 1 HB Filter
13
Resampler + 2 HB Filters
23
1 Halfband Filter
7
2 Halfband Filters
17
Bypass
0
l) When the Resampler is used, the number of processing clock
cycles is actually per output sample, but at decimation factors
close to 1.0, the filter buffer may overflow due to a long string
of computations.
4
The Coordinate converter requires 17 clocks to yield 16 bits
of accuracy on the phase and magnitude outputs. If new
input samples arrive prior to the completion of 17 clock
cycles, the calculation is terminated and the interim result is
latched with reduced resolution. The minimum accuracy
possible is approximately 5.5 bits for magnitude and 6.5 bits
for phase.
8. Discriminator FIR Filter
a) Input Sample Rate:
Equals the output sample rate of the
resampler/halfband block.
b) Compute Clock:
PROCCLK
c) Decimation:
1 to 8.
≤35MHz [≤55MHz].
d) The maximum number of taps is 63 for a symmetric filter and
32 for an asymmetric filter.
e) The equations for calculating the number of taps available,
(which is dependent on the processing clock, the input sample
rate, and the symmetry of the filter) are shown in Table 6.
TABLE 6. CALCULATION DISCRIMINATOR FIR TAP NUMBER
# of available
taps
SYMMETRIC,
EVEN # OF
TAPS
SYMMETRIC,
ODD # OF
TAPS
2 * (CLKS -R)
2 * (CLKS -R) -1 CLKS -R
ASYMMETRIC
Where CLKS = PROCCLK divided by the output sample rate of
the FIR (quotient truncated to nearest integer) and R is the
decimation factor.
f) Each coefficient bits has 22 bits.
g) The frequency detection is done by delaying and subtracting
(modulo 2π) the phase value from the cartesian to polar conversion block (dΦ/dt). The delay can range from 1 to 8 samples. At a delay of one, the range of the discriminator is
±(fIN /2). As the delay increases, the range decreases. For example, at a delay of 3, the detection range is ±(fIN/6).
h) There is a phase multiplier (modulo 2π) block preceding the
dΦ/dt calculation that can multiply the phase by 1, 2, 4, or 8 to
remove phase modulation before frequency detection. The
phase multiplication restricts the discriminator range by factors of 1, 2, 4 or 8.
i) The signal should be limited to a bandwidth less than the detection range of the discriminator or there may be frequency
wrap around (aliasing).
j) In the A and B versions of the HSP50214, the delayed and
subtracted phase, the magnitude, or the I output of the Resampler/Halfband block can be selected as the source for the input of the discriminator FIR. (See the HSP50214A/B Data
Sheets.
The Discriminator FIR filter output is provided at the
discriminator input sample rate, so that if the filter is
decimating, multiple data outputs will result until the
decimation requires the next output sample to appear.
DATARDY is asserted time aligned with and at the same
rate as the data type selected for the AOUT output.
Application Note 9720
The first design approach fixes the number of taps and
varies the out of band rejection and transition band until a
compliant design is implemented. The fixed number of filter
taps may be set because of some clocking restraint of one of
the filter blocks in the PDC or somewhere in the overall
system.
The second design approach sets an out of band
specification and varies the number of filter taps or the
transition band to create a compliant design.
The third design approach sets a fixed transition band
specification and varies the number of filter taps and the out
of band rejection, to create a compliant design. An overview
of these three approaches is illustrated in Figure 4.
The 255 tap FIR should be designed to have an output
bandwidth no greater than 1/4 of the FIR input sample rate.
This prevents the halfband filter from introducing interfering
alias signals in the band of interest. Excellent passband
dynamic range can be achieved when the bandwidth of
interest is less than 1/4 the HB5 Halfband Filter output
sample rate,
CIC OutputRate
f HB5 = ------------------------------------------------ ,
N
2
0<N<5
5
(EQ. 2)
LEAST
OUT OF BAND
REJECTION
MAGNITUDE
1. Begin with the FIR
The 255 tap FIR is a very important filter element in the PDC
because of all the PDC filter elements it provides the most
flexibility in establishing spectral shaping and complying with
the out of band rejection, passband bandwidth and transition
band specifications. The FIR establishes the narrowest
bandwidth in the downconverter, and thus its output rate is
related to the Nyquist rate of the bandwidth of interest in any
application. Three design parameters, 1) out of band
rejection, 2) transition bandwidth, and 3) number of taps,
offer three degrees of design freedom in approaching a
digital downconverter. These three degrees of freedom allow
optimizing dynamic range, sample rates, number of filter
taps and out of band rejection throughout the filter blocks in
the converter. All three approaches begin with the FIR filter
design. Many of the requirements for the FIR filter are set by
the transmit baseband filtering.
Use of the Interpolating Halfband Filters further down the
processing chain can allow the FIR to run at reduced rate to
maximize the number of taps available in the 255 tap FIR
filter.
MOST
OUT OF BAND
REJECTION
FREQUENCY
FIGURE 4A. FIXED NUMBER OF FILTER TAPS, VARIABLE
OUT OF BAND REJECTION, VARIABLE
TRANSITION BAND
20 TAPS
BW SPEC
40 TAPS
MAGNITUDE
The PDC contains an NCO/Mixer and six filter blocks which
can be configured for various applications. A natural
question to ask about the PDC is “What is the maximum
operation rate?” Because there are three internal clocks:
CLKIN for the front end blocks; PROCCLK for back end
blocks; and the Re-Sampling NCO clock for the Re-sampling
polyphase FIR, Interpolating Halfband filters, and output
blocks, the answer is not so simple. Likewise, determining
the maximum output bandwidth can be somewhat complex.
A top level approach to PDC configuration is necessary to
understand and to maximize the many features of each filter
block in this very flexible downconverter.
because it ensures significant attenuation of the composite
filter alias profile in the passband. Figure 5 illustrates such a
filter design.
60 TAPS
OUT OF BAND
REJECTION
SPEC
FREQUENCY
FIGURE 4B. FIXED OUT OF BAND REJECTION, VARIABLE
NUMBER OF FILTER TAPS, VARIABLE
TRANSITION BAND
TRANSITION
BAND
SPEC
MAGNITUDE
Design Approaches for the PDC
20 TAPS
40 TAPS
60 TAPS
FREQUENCY
FIGURE 4C. FIXED TRANSITION BAND, VARIABLE OUT OF
BAND REJECTION, VARIABLE NUMBER OF
FILTER TAPS
FIGURE 4. FREQUENCY DOMAIN VIEW OF DESIGN TRADES
Application Note 9720
USER BANDWIDTH WITH
HIGH DYNAMIC RANGE
(MINIMAL ALIAS INTERFERENCE)
CIC FILTER
ALIAS TERM
(WHEN ONLY 1 HB USED)
MAGNITUDE
HALFBAND
FILTER
ALIAS TERM
fS/8 fS/4
f’S/4 f’S/2
fS/2
f’S
3fS/4
3f’S/2
fS
2f’S
bandwidth reduction. Rate changes from 1 to 1/32 are
possible with bandwidth reductions of up to 1/32 using this
filter block. The halfband filters have a flatter passband and
a wider “alias free” output bandwidth than the CIC filter.
Use of this block requires an understanding of the alias profile
to ensure that the desired dynamic range is achieved prior to
entering the 255 tap FIR filter. Recall that the FIR filter
bandwidth was set to 1/8 of its input frequency to avoid the alias
images of the last halfband filter, which fall at 1/4 of the FIR
input sample rate. The effect of the alias on full dynamic range
is illustrated in Figure 6, which compares the full dynamic range
bandwidth of the first and last stage of the Halfband filter block.
By establishing a dynamic range specification, the bandwidth
can be selected from any combination of the halfband filters,
although the filters are typically enabled from stage 5 down to
stage 1, as increasing number of stages are required.
FREQUENCY
The Interpolation Halfbands offer the designer the ability to
oversample the resampled polyphase filtered data by twice
or four times the polyphase filter output rate. Thus, the rate
change of this filter block can vary from 0.25 to 4. These
halfband filters allow the 255 tap FIR filter to be run at a
lower rate to obtain more filter taps and then interpolated to
regain the time resolution. The output rate of this filter block
is the sample rate of the coordinate converter, the
discriminator, the discriminator FIR and the output block.
HB1 REQ
RESPONSE
HB1 ALIAS
HB5 ALIAS
HB5 FREQ
RESPONSE
FREQUENCY (NORMALIZED TO OUTPUT FREQUENCY)
FIGURE 6A.
FULL DYNAMIC RANGE BANDWIDTH
MAGNITUDE (dB)
2. Resampler and Interpolation Considerations
The second filter block to be considered is the Polyphase
Resampler FIR/ Interpolation Filters. While the 255 Tap FIR
establishes the bandwidth of interest, the Polyphase
Resampler/Interpolating Halfband filter is used to establish
the output rate of the PDC. The output sample rate of the
polyphase re-sampling filter is less than its input sample
rate. The rate change is set by the ratio of the Resampler
NCO frequency to the Resampler input sample rate. The
range of the rate change is from 1/4 to ~1, of fS , the
Resampler filter input sample rate. This value is not required
to be an integer! The 3dB passband of the polyphase
Resampler filter is located at 0.375 the Resampler filter input
sampling frequency. At 0.25 the Resampler input sampling
frequency greater than 60dB alias attenuation is achieved.
Use this filter to establish the non-integer rate changes from
the input sampler to the output (user) sample rate. The
Resampler NCO update rate is the input sample rate to the
Resampler filter.
HB5 FREQ
RESPONSE
HB5 ALIAS
FREQUENCY (NORMALIZED TO OUTPUT FREQUENCY)
FIGURE 6B.
FULL DYNAMIC RANGE BANDWIDTH
MAGNITUDE (dB)
FIGURE 5. RULE OF THUMB DESIGN OF FIR PASSBAND
MAGNITUDE (dB)
fS = HALFBAND FILTER #5 INPUT RATE
f’S = HALFBAND FILTER #5 OUTPUT RATE
HB1 FREQ
RESPONSE
HB1 ALIAS
3. Halfband Filter Considerations
The third filter block to be considered is HalfBand filter block.
The halfband filters are used to reduce the sampling rate
and bandwidth of the input signal. This filter block allows the
user to set an even multiple of 2 rate reduction and
6
FREQUENCY (NORMALIZED TO OUTPUT FREQUENCY)
FIGURE 6C.
FIGURE 6. HALFBAND FULL DYNAMIC RANGE BANDWIDTHS
Application Note 9720
4. CIC Filter Considerations [2]
The final filter stage to be considered is the CIC filter. The
CIC filter is the only filter stage that is running at the CLKIN
rate (when CLKIN > PROCCLK). This filter provides the rate
reduction necessary to meet the back end processing rate,
PROCCLK. This allows for maximum sampling speed into
the part. The CIC filter does rate reduction and out of band
signal filtering. The CIC filter response has a main lobe
extending to fS /R, where R is the decimation rate of the filter
and ranges from 4 to 32. These two constraints can be
opposing.
5. Filter Implementation Trades
With the initial pass of the PDC internal filter configuration
process complete, the next step is to optimize the filters.
Begin by verifying that all of the filter sample rates match at
the interfaces. Setting CLKIN high yields wider user
bandwidth and reduces the requirements on the analog antialiasing filter. Setting PROCCLK high yields filters with more
taps for a given filter input sample rate. These two
constraints can be opposing.
For example, if fSAMP, the FIR input sample rate, is set to a
few frequencies in GSM (multiples of the baud rate). The FIR
output sample rate must be a submultiple to find acceptable
FIR input sample rates and make sure it can be
implemented. Then check the alias of the halfband (BW <
1/4 fSAMPLE FIR).
Remember that the CLKIN rate limit is 52MHz [65MHz for
A/B], while the PROCCLK is 35MHz [55MHz for A/B]. This
means that the CLKIN input sample rate must be decimated
by at least 2 to make the interface compatible. PROCCLK
must always be greater than or equal to the CIC filter output
rate discussed in the Polyphase Re-Sampling filter section.
After configuring the filters, the next step is to confirm that the
dynamic range is acceptable. Finally, check the FIR filter taps
available and ensure that the out of band attenuation and
transition band filter performance are acceptable. The final
check is verify that the output rate is sufficient for the
application.
7
Detailed Filter Block Descriptions
Fifth Order CIC Filter
This filter has a minimum decimation rate of R = 4 and a
maximum decimation rate of R = 32 (Note 1). The minimum
rate of 4 is set by the hardware multiplex and throughput
delays. This section is clocked at CLKIN rate, defining the
maximum input rate as 52MSPS for the HSP50214 and
65MHz for the HSP50214A and B. Tables 7 and 7A detail the
maximum output rates for all CIC filter decimation factors.
The CIC delay is calculated as follows:
6CLKIN
CIC Delay = 5CLKIN + ----------------------R
6
CIC Delay = 5 + ---- ( CLKIN Period )
R
The 5CLKIN cycles is for the integrator and the 6CLKIN/R
cycles is for the COMB filter.
Application Note 9720
TABLE 7. CIC FILTER OUTPUT RATE vs DECIMATION
RATE FOR HSP50214
CIC
MODE
(NOTE 1)
DECIMATION
RATE (R)
(NOTE 2)
MAXIMUM
FILTER
OUTPUT RATE
(MSPS)
Bypass
-
CIC
TABLE 7A. CIC FILTER OUTPUT RATE vs DECIMATION
RATE FOR HSP50214A AND B
COMMENTS
CIC
MODE
(NOTE 3)
DECIMATION
RATE (R)
(NOTE 4)
MAXIMUM
FILTER
OUTPUT RATE
(MSPS)
52
No Decimation
Bypass
-
65
4
52/4 = 13.0
Minimum
Decimation is 4
CIC
4
65/4 = 16.25
CIC
5
52/5 = 10.4
CIC
5
65/5 = 13.00
CIC
6
52/6 = 8.67
CIC
6
65/6 = 10.83
CIC
7
52/7 = 7.43
CIC
7
65/7 = 9.29
CIC
8
52/8 = 6.50
CIC
8
65/8 = 8.13
CIC
9
52/9 = 5.78
CIC
9
65/9 = 7.22
CIC
10
52/10 = 5.20
CIC
10
65/10 = 6.50
CIC
11
52/11 = 4.73
CIC
11
65/11 = 5.91
CIC
12
52/12 = 4.33
CIC
12
65/12 = 5.42
CIC
13
52/13 = 4.00
CIC
13
65/13 = 5.00
CIC
14
52/14 = 3.71
CIC
14
65/14 = 4.64
CIC
15
52/15 = 3.47
CIC
15
65/15 = 4.33
CIC
16
52/16 = 3.25
CIC
16
65/16 = 4.06
CIC
17
52/17 = 3.06
CIC
17
65/17 = 3.82
CIC
18
52/18 = 2.89
CIC
18
65/18 = 3.61
CIC
19
52/19 = 2.74
CIC
19
65/19 = 3.42
CIC
20
52/20 = 2.60
CIC
20
65/20 = 3.25
CIC
21
52/21 = 2.48
CIC
21
65/21 = 3.10
CIC
22
52/22 = 2.36
CIC
22
65/22 = 2.95
CIC
23
52/23 = 2.26
CIC
23
65/23 = 2.83
CIC
24
52/24 = 2.17
CIC
24
65/24 = 2.71
CIC
25
52/25 = 2.08
CIC
25
65/25 = 2.60
CIC
26
52/26 = 2.00
CIC
26
65/26 = 2.50
CIC
27
52/27 = 1.93
CIC
27
65/27 = 2.41
CIC
28
52/28 = 1.86
CIC
28
65/28 = 2.32
CIC
29
52/29 = 1.79
CIC
29
65/29 = 2.24
CIC
30
52/30 = 1.73
CIC
30
65/30 = 2.17
CIC
31
52/31 = 1.68
CIC
31
65/31 = 2.10
CIC
32
52/32 = 1.63
CIC
32
65/32 = 2.03
Maximum
Decimation is 32
NOTES:
COMMENTS
No Decimation
Minimum
Decimation is 4
Maximum
Decimation is 32
NOTES:
1. It is possible to achieve a decimation of 64 using a 10-bit
converter shifted to the bottom of the input bits, a non-standard
configuration.
3. It is possible to achieve a decimation of 64 using a 10-bit
converter shifted to the bottom of the input bits, a non-standard
configuration.
2. The maximum rate may be limited in subsequent blocks.
4. The maximum rate may be limited in subsequent blocks.
8
Application Note 9720
Decimating Halfband Filters
fPROCCLK/fS ≥ [(7)(HB5)(2HB5) +
The decimating halfband filters are clocked by the PROCCLK,
which makes the maximum input rate for this filter section
equal to 35MHz. It is important that this section must be able
to support the output rate of the CIC section for proper
operation. Five selectable decimating halfband filters in this
block have progressively narrower alias free transition
bandwidths, ranging from 0.5 to 0.125 times the input sample
rate. The 6dB bandwidth of all five filters is 0.250 times the
input sample rate. Each halfband section will decimate by two,
(i.e., the output rate will be half the input rate). Note that the
filter sections may be enabled in any combination. Filters
should be selected based on the required transition band
steepness and acceptable clock rate. The equation used in
Tables 8 and 8A, to calculate the ratio of the PROCCLK to
Sample Rate is:
(6)(HB4)(2(HB4 + HB5)) +
(5)(HB3)(2(HB3 + HB4 + HB5)) +
(4)(HB2)(2(HB2 + HB3 + HB4 + HB5)) +
(3)(HB1)(2(HB1 + HB2 + HB3 + HB4 + HB5))]/2T
(EQ. 3)
where
HB1 = 1 if HB1 is selected and 0 if it is bypassed;
HB2 = 1 if HB2 is selected and 0 if it is bypassed
HB3 = 1 if HB3 is selected and 0 if it is bypassed
HB4 = 1 if HB4 is selected and 0 if it is bypassed
HB5 = 1 if HB5 is selected and 0 if it is bypassed
T = number of Halfband Filters. The range for T is (0-5).
TABLE 8. DECIMATING HALFBAND MAXIMUM OUTPUT RATES vs CONFIGURATION
HALFBAND FILTER
SECTION NUMBER
5
4
3
2
0
0
0
1
0
0
0
1
1
1
0
1
OVERCLOCK RATE
MAXIMUM INPUT
FACTOR
SAMPLE RATE (MHz)
MODE
MAXIMUM OUTPUT
RATE (MHz)
Activated Halfband Filter
FPR = 35MHz
1
(FPR/fS)
FPR = 35MHz
0
0
1.00
35.00
Bypass - None
35.00
0
0
7.00
5.000
HB5
2.500
0
0
0
6.00
5.853
HB4
2.917
0
0
0
9.50
3.684
HB5 and HB4
0.921
0
1
0
0
5.00
7.000
HB3
3.500
0
1
0
0
8.50
4.4118
HB5 and HB3
1.029
0
1
1
0
0
8.00
4.375
HB4 and HB3
1.084
1
1
1
0
0
9.75
3.590
HB5, HB4 and HB3
0.449
0
0
0
1
0
4.00
8.750
HB2
4.375
1
0
0
1
0
7.50
4.667
HB5 and HB2
1.167
0
1
0
1
0
7.00
5.000
HB4 and HB2
1.250
1
1
0
1
0
8.75
4.000
HB5, HB4 and HB2
0.500
0
0
1
1
0
6.50
5.385
HB3 and HB2
1.346
1
0
1
1
0
8.25
4.242
HB5, HB3 and HB2
0.530
0
1
1
1
0
8.00
4.375
HB2, HB3 and HB4
0.547
1
1
1
1
0
8.88
3.944
HB5, HB4, HB3 and HB2
0.247
0
0
0
0
1
3.00
11.667
HB1
5.833
1
0
0
0
1
6.50
5.385
HB5 and HB1
1.346
0
1
0
0
1
6.00
5.833
HB4 and HB1
1.458
1
1
0
0
1
7.75
4.516
HB5, HB4 and HB1
0.565
0
0
1
0
1
5.50
6.364
HB3 and HB1
1.591
1
0
1
0
1
7.25
4.828
HB5, HB3 and HB1
0.603
0
1
1
0
1
7.00
5.000
HB4, HB3 and HB1
0.625
1
1
1
0
1
7.88
4.444
HB5, HB4, HB3 and HB1
0.278
0
0
0
1
1
5.00
7.000
HB2 and HB1
1.750
1
0
0
1
1
6.75
5.185
HB5, HB2 and HB1
0.648
0
1
0
1
1
6.50
5.385
HB4, HB2 and HB1
0.673
1
1
0
1
1
7.38
4.746
HB5, HB4, HB2 and HB1
0.297
0
0
1
1
1
6.25
5.600
HB3, HB2 and HB1
0.700
1
0
1
1
1
7.13
4.912
HB4, HB3, HB2 and HB1
0.307
0
1
1
1
1
7.00
5.000
HB4, HB3, HB2 and HB1
0.313
1
1
1
1
1
7.44
4.706
HB5, HB4, HB3, HB2 and HB1
0.147
9
Application Note 9720
TABLE 8A. DECIMATING HALFBAND MAXIMUM OUTPUT RATES vs CONFIGURATION
HALFBAND FILTER
SECTION NUMBER
OVERCLOCK RATE
MAXIMUM INPUT
FACTOR
SAMPLE RATE (MHz)
MODE
MAXIMUM OUTPUT
RATE (MHz)
Activated Halfband Filter
FPR = 55MHz
5
4
3
2
1
(FPR/fS)
FPR = 55MHz
0
0
0
0
0
1.00
55.00
Bypass - None
55.00
1
0
0
0
0
7.00
7.857
HB5
3.929
0
1
0
0
0
6.00
9.167
HB4
4.583
1
1
0
0
0
9.50
5.789
HB5 and HB4
1.447
0
0
1
0
0
5.00
11.000
HB3
5.500
1
0
1
0
0
8.50
6.471
HB5 and HB3
1.618
0
1
1
0
0
8.00
6.875
HB4 and HB3
1.719
1
1
1
0
0
9.75
5.641
HB5, HB4 and HB3
0.705
0
0
0
1
0
4.00
13.750
HB2
6.875
1
0
0
1
0
7.50
7.333
HB5 and HB2
1.833
0
1
0
1
0
7.00
7.857
HB4 and HB2
1.964
1
1
0
1
0
8.88
6.197
HB5, HB4 and HB2
0.387
0
0
1
1
0
6.50
8.462
HB3 and HB2
2.115
1
0
1
1
0
8.25
6.667
HB5, HB3 and HB2
0.833
0
1
1
1
0
8.00
6.875
HB2, HB3 and HB4
0.859
1
1
1
1
0
8.88
6.197
HB5, HB4, HB3 and HB2
0.387
0
0
0
0
1
3.00
18.333
HB1
9.167
1
0
0
0
1
6.50
8.462
HB5 and HB1
2.115
0
1
0
0
1
6.00
9.167
HB4 and HB1
2.292
1
1
0
0
1
7.75
7.097
HB5, HB4 and HB1
0.887
0
0
1
0
1
5.50
10.000
HB3 and HB1
2.500
1
0
1
0
1
7.25
7.586
HB5, HB3 and HB1
0.948
0
1
1
0
1
7.00
7.857
HB4, HB3 and HB1
0.982
1
1
1
0
1
7.88
6.984
HB5, HB4, HB3 and HB1
0.437
0
0
0
1
1
5.00
11.000
HB2 and HB1
2.750
1
0
0
1
1
6.75
8.148
HB5, HB2 and HB1
1.019
0
1
0
1
1
6.50
8.462
HB4, HB2 and HB1
1.058
1
1
0
1
1
7.38
7.458
HB5, HB4, HB2 and HB1
0.466
0
0
1
1
1
6.25
8.800
HB3, HB2 and HB1
1.100
1
0
1
1
1
7.13
7.719
HB4, HB3, HB2 and HB1
0.482
0
1
1
1
1
7.00
7.857
HB4, HB3, HB2 and HB1
0.491
1
1
1
1
1
7.44
7.395
HB5, HB4, HB3, HB2 and HB1
0.231
10
Application Note 9720
255 TAP FIR Filter
The 255 TAP FIR filter has a minimum decimation factor of R
= 1. The maximum decimation factor in this filter is R = 16.
The filter can be “effectively” bypassed by setting C0 = 1 and
CN = 0. This requires three clock cycles. The filter is clocked
by PROCCLK, so the maximum input rate is 35MHz for the
HSP50214 and 55MHz for the HSP50214A and B. One
clock is used to write data into the ROM.
1. Determining the Number of FIR Filter Taps
For the generic filter configuration, use Equation 4 to
calculate the number of taps available at a given input
sample rate. We can use Equation 5 to calculate the
maximum input rate, and Equation 6 to calculate the
maximum output rate.
Taps = floor[PROCCLK/(F SAMP ⁄ R ) – R ] •
( 1 + SYM ) – ( SYM • ODD ) for real filters )
(EQ. 4A)
FILTER TYPE
(EQ. 4B)
where floor is defined as the integer portion of a number;
PROCCLK is the compute clock; fSAMP = the FIR input
sample rate; R = Decimation Rate; SYM = 1 for symmetrical
filter, 0 for asymmetrical filter; ODD = 1 for an odd number of
filter taps, 0 = an even number of taps.
PDC FIR Filter Number of Taps Calculation
Table 9 details the formula for four common filter types.
Tables 10 and 11 detail the rates at which a “maximum
number of taps” filter can run, for minimum and maximum
FIR decimation factors.
TABLE 9.
EQUATION FOR NUMBER OF
FILTER TAPS
Real, Symmetric, Even # Taps [PROCCLKS/fSAMP /R) -R]*2
EQUATION FOR NUMBER OF FILTER TAPS
Real,
[PROCCLK/(fSAMP/R) -R]*2
Symmetric,
[55 x 106/(6.154 x 106/16) -16] *2 = 254
Even # of Taps
Real,
Symmetric,
Odd # of Taps
[{PROCCLK/(fSAMP/R) -R} -1*2
[{55 x106 /(6.154 X 106 /16) -16} -1] *2 = 252
Real,
Asymmetric
[PROCCLK/(fSAMP/R) -R]
[55 x 106 /(6.154 x 106 /16) -16] = 127
Complex
[PROCCLK/(fSAMP/R) -R]/2
[55 x 106/(6.154 x 106/16 -16]/2 = 63
TABLE 11. EXAMPLE FOR PROCCLK = 55MHz; FSAMP =
0.430MHz; R = 1
FILTER TYPE
Taps = floor [ ( PROCCLK ⁄ F SAMP ⁄ R ) – R ) ⁄ 2 ] for complex filters
FILTER TYPE
TABLE 10. EXAMPLE FOR PROCCLK = 55MHz,
fSAMP = 5MHz; R = 16
EQUATION FOR NUMBER OF FILTER TAPS
Real,
Symmetric,
Even # Taps
[PROCCLKS/fSAMP/R) -R]*2
[55 X 106/(0.430 x 106/1) -1]*2 = 254
Real,
Symmetric,
Odd # Taps
[{PROCCLKS/fSAMP/R) -R} -1]*2
[{55 x 10 6 /(0.430 x 10 6 /1) -1} -1]*2 = 252
Real,
Symmetric
[PROCCLKS/fSAMP/R) -R]
[55 x 106 /(0.430 x 106 /1) -1] = 127
Complex
[PROCCLKS/(fSAMP/R) -R]/2
[55 x106 /(0.430 x 106 /1) -1]/2 = 63
Example FIR Filter “Number of Taps” Calculation
As an example, for a 35MHz compute clock, a 5MHz input
sample rate, decimation by 2, even symmetry, and an odd
number of taps, the number of taps is:
Taps = floor[35MHz ⁄ ( 5MHz ⁄ 2 ) – 2 ] • ( 1 + 1 ) – ( 1 • 1 ) =
floor [ 14 – 2 ] • 2 – 1 = 12 • 2 – 1 = 23 for a real filter and
Real, Symmetric, Odd # Taps
[{PROCCLKS/fSAMP /R) -R} -1]*2
Taps = floor[(35MHz ⁄ ( 5MHz ⁄ 2 ) – 2 ) ⁄ 2 ] =
floor [ ( 14 – 2 ] ⁄ 2 ] = 6 for a complex filter
Real, Asymmetric
[PROCCLKS/(fSAMP /R) -R]
2. Calculating the Maximum Input Sample Rate
Complex
[PROCCLKS/fSAMP /R) -R]/2
We can rearrange Equations 4 and 4A to yield the maximum
input sample rate.
Where:
PROCCLK is the PDC backend compute clock,
fSAMP is the FIR input sample clock,
R is the FIR decimation factor.
PROCCLKS/(fSAMP/R) is the number of clocks required to
generate a FIR output.
11
f SAMP = PROCCLK • ( R ) ⁄ [ R + [ ( Taps ) +
( SYM • ODD ) ] ⁄ ( 1 + SYM ) ] for real filters
f SAMP = PROCCLK • R ⁄ [ R + [ ( Taps ) • 2 ] ]
for complex filters
(EQ. 5A)
(EQ. 5B)
where PROCCLK is the compute clock; fSAMP = the FIR
input sample rate; R = Decimation Rate; SYM = 1 for
symmetrical filter, 0 for asymmetrical filter; ODD = 1 for an
odd number of filter taps, 0 = an even number of taps.
Application Note 9720
Example Maximum Input Rate Calculation
Let’s use the example provided above to see if we can
predict the 5MHz input rate.
fSAMP = 35MHz*(2)/[2 + [(23)+(1)]/(2)] = 5.00MHz, which is
correct.
3. Calculating the Maximum Output Rate
The equation for the maximum output sample rate becomes:
f FIROUT = ( f SAMP ) ⁄ R
(EQ. 6)
for both real and complex filters.
An Example Maximum Output Rate Calculation
As an example, for a compute clock of 35MHz and a real,
symmetrical filter, no decimation, all 255 taps can be used
for output sample rates of 272.37kHz. If that same filter
decimates by 16, then the output sample rate becomes
272.37/16 = 17.023kHz.
Table 12 and 12A provides a sampling of the filter output
rate calculations. The maximum output rate as a function of
a real symmetric 127 tap filter configuration with varying
decimation rates is given. Use of Equations 4, 5 and 6
provide the details necessary to calculate an application
specific filter configuration. Remember that prior to obtaining
a part level operational configuration, the input rate of the
255 tap FIR Filter section must match the output rate of the
Halfband filter section.
Figures 7 and 8 provide a plot of Input Rate and Output Rate
as a function of Decimation Rate for a set of odd number of
tap, symmetric filters (15, 31, 63, 127, 191 and 255). They will
help in estimating input and output rates if the filter is known.
Another approach is to determine the number of filter taps that
can be implemented at a specific input rate. Figures 9 through
12A are plots of the number of filter taps based on the input
rate. Each figure represents a different decimation rate (R = 1,
2, 4, 8, and 16). These plots will help determine the extent of
shaping that can be done with the FIR filter for the specific
input rate.
TABLE 12. MAXIMUM OUTPUT RATE vs FIR FILTER CONFIGURATION
MODE
DECIMATION
(R)
REAL OR
COMPLEX
SYMMETRIC OR
ASYMMETRIC
NUMBER OF
TAPS
MAXIMUM INPUT
SAMPLE RATE
(MHz)
MAXIMUM
OUTPUT RATE
(MHz)
Bypass
1
Real
-
1
5.83 (Notes 5, 6)
5.83 (Notes 5, 6)
Filter
2
Real
Symmetric
127
1.060606
0.530303
Filter
3
Real
Symmetric
127
1.567164
0.522388
Filter
4
Real
Symmetric
127
2.058824
0.514706
Filter
5
Real
Symmetric
127
2.536232
0.507246
Filter
6
Real
Symmetric
127
3.000000
0.500000
Filter
7
Real
Symmetric
127
3.450704
0.492958
Filter
8
Real
Symmetric
127
3.888889
0.486111
Filter
9
Real
Symmetric
127
4.315068
0.479452
Filter
10
Real
Symmetric
127
4.729730
0.472973
Filter
11
Real
Symmetric
127
5.133333
0.466667
Filter
12
Real
Symmetric
127
5.526316
0.460526
Filter
13
Real
Symmetric
127
5.909091
0.454545
Filter
14
Real
Symmetric
127
6.282051
0.448718
Filter
15
Real
Symmetric
127
6.645570
0.443038
Filter
16
Real
Symmetric
127
7.000000
0.4375
(Note 6)
NOTES:
5. Assumes a 35MHz PROCCLK.
6. Since 6 CLKS are required by AGC logic, max CLK = 35MHz/6 = 5.83MHz, which is lower than the rate calculated for a FIR bypass (35MHz/3
= 11.67).
12
Application Note 9720
TABLE 12A. MAXIMUM OUTPUT RATE vs FIR FILTER CONFIGURATION
MODE
DECIMATION
(R)
REAL OR
COMPLEX
SYMMETRIC OR
ASYMMETRIC
NUMBER OF
TAPS
MAXIMUM INPUT
SAMPLE RATE
(MHz)
MAXIMUM
OUTPUT RATE
(MHz)
Bypass
1
Real
-
1
9.17 (Notes 7, 8)
9.17 (Notes 7, 8)
Filter
2
Real
Symmetric
127
1.667
0.833
Filter
3
Real
Symmetric
127
2.463
0.821
Filter
4
Real
Symmetric
127
3.235
0.809
Filter
5
Real
Symmetric
127
3.986
0.797
Filter
6
Real
Symmetric
127
4.714
0.786
Filter
7
Real
Symmetric
127
5.423
0.775
Filter
8
Real
Symmetric
127
6.111
0.764
Filter
9
Real
Symmetric
127
6.781
0.753
Filter
10
Real
Symmetric
127
7.432
0.743
Filter
11
Real
Symmetric
127
8.067
0.733
Filter
12
Real
Symmetric
127
8.684
0.724
Filter
13
Real
Symmetric
127
9.286
0.714
Filter
14
Real
Symmetric
127
9.872
0.705
Filter
15
Real
Symmetric
127
10.433
0.696
Filter
16
Real
Symmetric
127
11.000
0.688
(Note 8)
NOTES:
7. Assumes a 55MHz PROCCLK.
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
INPUT RATE
OUTPUT RATE
16-TAP
8-TAP
8-TAP
1
I/O RATE (MHz)
I/O RATE (MHz)
8. Since 6 CLKS are required by AGC logic, max CLK = 55MHz/6 = 9.17MHz, which is lower than the rate calculated for a FIR bypass
(55/3 = 18.33MHz).
32-TAP
64-TAP
2
3
4
DECIMATION RATE
FIGURE 7. DETERMINING MAXIMUM INPUT AND OUTPUT
RATES BASED ON FILTER DECIMATION FOR A
8, 16, 32 AND 64 TAP FILTER (fS = 33MHz, SYM = 1,
EVEN/ODD = 0)
13
28
27
26
25
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
INPUT RATE
OUTPUT RATE
8-TAP
8-TAP
16-TAP
32-TAP
16-TAP
32-TAP
64-TAP
64-TAP
1
2
3
DECIMATION RATE
FIGURE 7A. DETERMINING MAXIMUM INPUT AND OUTPUT
RATES BASED ON FILTER DECIMATION FOR A
8, 16, 32 AND 64 TAP FILTER (fS = 55MHz,
SYM = 1, EVEN/ODD = 0)
4
Application Note 9720
2.0
3.5
INPUT RATE
OUTPUT RATE
1.5
2.5
1.0
128-TAP
I/O RATE (MHz)
I/O RATE (MHz)
INPUT RATE
OUTPUT RATE
3.0
192-TAP
255-TAP
2.0
128-TAP
1.5
192-TAP
255-TAP
1.0
0.5
0.5
0
1
2
3
DECIMATION RATE
0
4
FIGURE 8. DETERMINING MAXIMUM INPUT AND OUTPUT
RATES, BASED ON FILTER DECIMATION FOR A
127, 192 AND 255 TAP FILTER (fS = 33MHz,
SYM = 1, EVEN/ODD = 0)
1
7
fS = 55MHz
6
FIR FILTER INPUT RATE (MHz)
FIR FILTER INPUT RATE (MHz)
fS = 35MHz
5
4
3
2
1
6
5
4
3
2
1
0
0
0 16 32 48 64 80 96 112 128 144 160 176 192 208 224 240
NUMBER OF FIR FILTER TAPS (1-255)
FIGURE 9. THE NUMBER OF FILTER TAPS vs INPUT RATE
FOR A DECIMATION OF 2, SYM = 1, EVEN/ODD = 0
0
16 32 48 64 80 96 112 128 144 160 176 192 208 224 240
NUMBER OF FIR FILTER TAPS (1-255)
FIGURE 9A. THE NUMBER OF FILTER TAPS vs INPUT RATE
FOR A DECIMATION OF 2, SYM = 1, EVEN/ODD = 0
7
7
fS = 35MHz
6
FIR FILTER INPUT RATE (MHz)
FIR FILTER INPUT RATE (MHz)
4
FIGURE 8A. DETERMINING MAXIMUM INPUT AND OUTPUT
RATES, BASED ON FILTER DECIMATION FOR A
127, 192 AND 255 TAP FILTER (fS = 55MHz,
SYM = 1, EVEN/ODD = 0)
7
5
4
3
2
1
0
2
3
DECIMATION RATE
fS = 55MHz
6
5
4
3
2
1
0
0 16 32 48 64 80 96 112 128 144 160 176 192 208 224 240
NUMBER OF FIR FILTER TAPS (1-255)
FIGURE 10. THE NUMBER OF FILTER TAPS vs INPUT RATE
FOR A DECIMATION OF 4, SYM = 1, EVEN/ODD = 0
14
0
16 32 48 64 80 96 112 128 144 160 176 192 208 224 240
NUMBER OF FIR FILTER TAPS (1-255)
FIGURE 10A. THE NUMBER OF FILTER TAPS vs INPUT RATE
FOR A DECIMATION OF 4, SYM = 1, EVEN/ODD = 0
Application Note 9720
7
7
fS = 55MHz
6
FIR FILTER INPUT RATE (MHz)
FIR FILTER INPUT RATE (MHz)
fS = 35MHz
5
4
3
2
1
6
5
4
3
2
1
0
0
0
0 16 32 48 64 80 96 112 128 144 160 176 192 208 224 240
NUMBER OF FIR FILTER TAPS (1-255)
FIGURE 11. THE NUMBER OF FILTER TAPS vs INPUT RATE
FOR A DECIMATION OF 8, SYM = 1, EVEN/ODD = 0
16 32 48 64 80 96 112 128 144 160 176 192 208 224 240
NUMBER OF FIR FILTER TAPS (1-255)
FIGURE 11A. THE NUMBER OF FILTER TAPS vs INPUT RATE
FOR A DECIMATION OF 8, SYM = 1, EVEN/ODD = 0
7
7
6
5
4
3
2
1
0
fS = 55MHz
FIR FILTER INPUT RATE (MHz)
FIR FILTER INPUT RATE (MHz)
fS = 35MHz
0
16 32 48 64 80 96 112 128 144 160 176 192 208 224 240
NUMBER OF FIR FILTER TAPS (1-255)
FIGURE 12. THE NUMBER OF FILTER TAPS vs INPUT RATE
FOR A DECIMATION OF 16
AGC Multipliers
The data multiplication by the AGC involves multiplexing and
delay circuitry resulting an output to input clock ratio of 6.
Since the circuitry is clocked by PROCCLK, the maximum
input rate is 35MHz, yielding a maximum output rate of
35/6 = 5.833MHz. Tables 13 and 13A detail this rate
transfer.
TABLE 13. MAXIMUM INPUT AND OUTPUT RATES OF THE
AGC MULTIPLIERS
MAX INPUT RATE (MHz)
MAX OUTPUT RATE (MHz)
35.00
5.833
TABLE 13A. MAXIMUM INPUT AND OUTPUT RATES OF THE
AGC MULTIPLIERS
MAX INPUT RATE (MHz)
MAX OUTPUT RATE (MHz)
55.00
9.167
15
6
5
4
3
2
1
0
0
16 32 48 64 80 96 112 128 144 160 176 192 208 224 240
NUMBER OF FIR FILTER TAPS (1-255)
FIGURE 12A. THE NUMBER OF FILTER TAPS vs INPUT RATE
FOR A DECIMATION OF 16
Polyphase Filters and Interpolating
Halfband Filters
The polyphase (Resampler) filter and interpolating halfband
filters will be considered a block. The polyphase filter is
clocked by PROCCLK and enabled by the Resampler NCO,
which is set via processor control. Equation 7 details the
calculation of the Resampler NCO Carry Output frequency.
The output sample rate is determined by the Resample
NCO.
f CO = f S × ( TCF + TOF ) ⁄ 2
32
(EQ. 7)
where fCO =; fS = Resampler NCO Clock Frequency (FIR
output rate); TCF = Timing Center Frequency; and TOF =
Timing Offset Frequency. TCF is processor programmed
and TOF is input via the serial interface. Both TCF and TOF
Application Note 9720
are 32-bit word values (0 < x < 4,294,967,295). The
maximum output rate is 0.999. . . X input rate.
TABLE 14A. POLYPHASE FILTER AND INTERPOLATING
HALFBAND FILTER MAX OUTPUT RATES
CLOCK
CYCLES
INPUT
RATE
(MHz)
INTERPO
LATION
RATE
MAX
OUTPUT
RATE
(MHz)
Bypass
0
55.000
-
55.000
Polyphase
Filter
6
55/6 = 9.17
-
9.17
Polyphase and
1 Halfband
Filter
13
55/13 = 4.23
2
8.46
Polyphase and
2 Halfband
Filters
23
55/23 = 2.39
4
9.56
1 Halfband
Filter
7
55/7 = 7.86
2
15.71
2 Halfband
Filters
17
55/17 = 3.24
4
12.94
The halfband filters are clocked by PROCCLK.
Emptying the filters requires a certain number of
PROCCLKs, depending on which filters are enabled. The
number of cycles, as well as the maximum I/O rates, are
shown in Table 14.
TABLE 14. POLYPHASE FILTER AND INTERPOLATING
HALFBAND FILTER MAX OUTPUT RATES
CLOCK
CYCLES
INPUT
RATE
(MHz)
INTERPO
LATION
RATE
MAX
OUTPUT
RATE
(MHz)
Bypass
0
35.000
-
35.000
Polyphase
Filter
6
35/6 = 5.833
-
NCO
(5.833)
Polyphase and
1 Halfband
Filter
13
35/13 =
2.692
2
NCO
(5.385)
Polyphase and
2 Halfband
Filters
23
35/23 =
1.522
4
NCO
(6.087)
1 Halfband
Filter
7
35/7 = 5.00
2
10.000
2 Halfband
Filters
17
35/17 =
2.059
4
8.235
MODE
MODE
NOTE: This frequency is set by the Resampler NCO.
Cartesian to Polar Converter
The maximum output rate of the Cartesian to Polar
Converter is a function of the precision desired in the
answer. This circuitry is clocked by PROCCLK, so the
maximum input rate is 35MHz for the HSP50214 and
55MHz for the HSP50214A and B. To obtain full accuracy
of 16 bits, 17 clocks are required. The maximum output rate
is 35/17 = 2.059MHz; 55/ 17 = 3.235MHz.
Tables 15 and 15A detail the output resolution based on the
maximum output clock, assuming the input is sampled at
35MHz and 55MHz, respectively. Six bits may be sufficient
for many applications. In general the resolution on the phase
output will need to be greater than on the magnitude output.
16
Application Note 9720
TABLE 15. BIT RESOLUTION AS A FUNCTION OF
INPUT/OUTPUT RATE INTO THE CONVERTER
TABLE 15A. BIT RESOLUTION AS A FUNCTION OF
INPUT/OUTPUT RATE INTO THE CONVERTER
INPUT
RATE
(MHz)
OUTPUT
RATE
(MHz)
MAGNITUDE
OUTPUT ERROR
(%)
PHASE OUTPUT
ACCURACY
(DEGREES)
INPUT
RATE
(MHz)
OUTPUT
RATE
(MHz)
MAGNITUDE
OUTPUT ERROR
(%)
PHASE OUTPUT
ACCURACY
(DEGREES)
35
35.000
-
-
55
55.000
-
-
35
17.500
14.12
45
55
27.500
14.12
45
35
11.667
3.98
26.565
55
18.333
3.98
26.565
35
8.750
1.03
14.036
55
13.750
1.03
14.036
35
7.000
0.26
7.125
55
11.000
0.26
7.125
35
5.833
0.07
3.576
55
9.167
0.07
3.576
35
5.00
0.02
1.790
55
7.857
0.02
1.790
35
4.375
0.004
0.895
55
6.857
0.004
0.895
35
3.889
Less than 0.004
0.447
55
6.111
Less than 0.004
0.447
35
3.500
Less than 0.004
0.224
55
5.500
Less than 0.004
0.224
35
3.182
Less than 0.004
0.112
55
5.000
Less than 0.004
0.112
35
2.916
Less than 0.004
0.056
55
4.583
Less than 0.004
0.056
35
2.688
Less than 0.004
0.028
55
4.231
Less than 0.004
0.028
35
2.500
Less than 0.004
0.014
55
3.929
Less than 0.004
0.014
35
2.333
Less than 0.004
0.007
55
3.667
Less than 0.004
0.007
35
2.188
Less than 0.004
0.003
55
3.438
Less than 0.004
0.003
NOTE: This table assumes full scale input.
NOTE: This table assumes full scale input.
References
For Intersil documents available on the internet, see web site
http://www.intersil.com.
[1] HSP50214 Data Sheet, Intersil Corporation, FN4266.
[2] Hogenauer, Eugene, “An Economical Class of Digital
Filters for Decimation and Interpolation”, IEEE
Transactions on Acoustics, Speech and Signal
Processing, Vol. ASSP-29 No. 2, April 1981.
[3] FO-006.1 HSP50214 Block Diagram,
Intersil Corporation
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17