AD9853_15 datasheet(19/31 Pages) AD

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OBSOLETE

AD9853

–19–

REV. C

The frequency response, H(f), of a CIC filter is found by evalu-

ating H(z) at z = e

j(2

πf/R):

jf R k

()













−

()

−

∑ 2

where f is relative to the input sample rate of the CIC filter.

With this formula, we can accurately predict the frequency

response of the CIC filters.

Compensating for CIC Roll-Off

As discussed previously, the CIC filters offer a low-pass charac-

teristic that can be used to eliminate the spectral images pro-

duced by the FIR filters. Unfortunately, the CIC response is not

flat over the frequency range of the baseband signal. Thus, the

inherent attenuation (or roll-off) of the CIC filters distorts the

baseband data signal. So even though the CIC filters help to

eliminate the images described earlier, they introduce another

form of error to the baseband signal—frequency-dependent

amplitude distortion. This ultimately manifests itself as a higher

level of Error Vector Magnitude (EVM) at the output of the

I and Q modulator. Also, the larger the bandwidth of the

baseband signal, the more pronounced the CIC roll-off, the

greater the amplitude distortion and the worse the EVM perfor-

mance. This is a serious problem because if a value of

α =1 is

used for the SRRC response of the FIR filters, a doubling of the

bandwidth of the baseband signal results and hence, a degrada-

tion in EVM performance.

Fortunately, there is a way to compensate for the effects of CIC

roll-off. Since the frequency response of the CIC filters is pre-

dictable, it is possible to compensate for the CIC roll-off charac-

teristic by adjusting the response of the FIR filters accordingly.

The adjustment is accomplished by modifying the FIR filter

response with a response that is the inverse of that of the CIC

filters. This is done by precompensating the FIR filters.

To perform CIC compensation, we simply define a function

(HCOMP) that has a response which is the inverse of the CIC

response. Specifically,

COMP

() = ()1

By multiplying the original FIR filter frequency response by

HCOMP, we obtain the necessary compensation.

Unfortunately, it’s not quite this simple. Recall that the coeffi-

cients of the baseband filter were computed using an inverse

Fourier transform integral which included the SRRC function.

In order to compensate for the CIC filter response, the SRRC

function must be multiplied by the HCOMP function. But the

frequency scale of the SRRC response is computed based on

frequencies relative to the symbol rate, while the HCOMP func-

tion is computed relative to the input sampling rate of the CIC

filter. The input CIC sampling rate happens to be the same as

the sample rate of the FIR filter (see Figure 36), or four times

the symbol rate. Thus, we have a frequency scaling problem.

This problem is easily corrected by introducing a frequency

scaling factor (FreqScale = 4) into the HCOMP function so that

the frequency scales of the two functions match. Thus, the

actual HCOMP function required is given by:

FreqScale

COMP =













It should be noted that in compensating for the CIC roll-off,

only the first stage CIC filter need be considered. This is due to

the fact that at the output of the first stage CIC filter the

bandwidth of the signal is reduced to the point that the roll-off

introduced by the second stage is negligible in the region of the

baseband signal.

The CIC compensation method is demonstrated by example

(using MathCad) in Figures 34 and 35. An interpolation rate

(R) of 6 is used in the example. The improvement obtained by

compensating for the CIC response is graphically demonstrated

in Figure 35 which shows:

• the SRRC filter response (which is the desired overall response)

• the composite response of the SRRC in series with the CIC

filter (distorted response)

• the composite response of the compensated SRRC in series

with the CIC (corrected response)

Note that the ideal SRRC response and the compensated com-

posite response are virtually identical in the region of the pass-

band. Thus, the goal of correcting for the CIC filter response

has been accomplished.

There is one subtlety to be noted in the example. The CIC

compensation is only applied to the first 90% of the bandwidth

of the baseband signal (note the variable

inside the integral).

It was found that compensation over the full 100% of the band-

width produced a reduction in the suppression of signals in the

stopband region of the SRRC. This resulted in creating more

distortion than by not correcting for the CIC roll-off in the first

place. However, by slightly reducing the bandwidth over which

correction is applied, the stopband suppression is once again

restored and a significant improvement in EVM performance is

obtained.

Determining the Necessary Interpolator Rate Change Ratio

The AD9853 contains three stages of digital interpolation:

1) Fixed 4

× Pulse Shaping FIR Filter.

2) Programmable 3 to 31 First Interpolation Filter.

3) Programmable 2 to 63 Second Interpolation Filter.

After the serial input data stream has been encoded into QPSK

or 16-QAM symbols, the symbol interpolation rate of the AD9853

is determined by the product of the three interpolating stages

listed above. In QPSK mode, the minimum symbol interpolation

rate that will work is 4

× 3 × 2 = 24; for 16-QAM the minimum

is 4

× 4 × 3 = 48. The maximum symbol interpolation rate is

× 31 × 63 = 7812. The symbol rate at the encoder output for

QPSK is equal to 1/2 the bit rate of the data and for 16-QAM it

is 1/4 the bit rate. Figure 36 is a partial block diagram of the

AD9853 and follows the path of the data stream from the input

of the I and Q encoder block to the output of the DAC.

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