Mis-Matches Minimization in 4-Channel TI-ADC using Fx-LMS Algorithm and FIR Filter Implementation

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International Journal of Emerging Technology and Advanced Engineering

Website: www.ijetae.com (ISSN 2250-2459,ISO 9001:2008 Certified Journal, Volume 4, Issue 5, May 2014)

909

Mis-Matches Minimization in 4-Channel TI-ADC

using Fx-LMS Algorithm and FIR Filter Implementation

Vandana Patel

1

, Prof. Navneet Kour

2

Department of Electronics & Communication Engg., Sagar Institute of Research and Technology, Bhopal

Abstract - Time Interleaved Analog-to-Digital Converters are integrated components of modern electronic circuits and facilitate the digital communication technology for realizing high-speed communication systems. Current Mobile and Wireless System is one of the milestone for wireless communication requiring ADCs. TI-ADC is an useful technique for implementation of efficient receivers with large frequency band. The act of TI-ADC is practically narrowed by errors due to mismatches taking place between channels, which leads to a significant humiliation in overall performance. In this paper we are working on all the four possible mismatches can be occurred in four channel TI-ADC which highly degrade the system performance and these mismatches can be timing mismatches, frequency mismatches, offset mismatches, and gain mismatches. The reason of mismatch occurrences is identical TI- ADC ICs are not having same characteristics and these mismatches increases when multiple chips are used in a system e.g. multiple channels in TI-ADC. Here we are presenting an technique which minimizes the various mismatches in four channel TI-ADC. For achieving this, we implement FIR Band Pass Filter with Fx-LMS algorithm and this methodology significantly minimizes the affects mismatches in TI-ADC.

Keywords- Four Channel Time Interleaved Analog to Digital Converters (TI-ADC), FIR Band Pass Filter, Time, Gain, Offset and Frequency Mismatches.

I. INTRODUCTION

[image:1.595.329.547.518.662.2] [image:1.595.63.289.599.641.2]

The performance of today’s communication system highly depends on the used analog-to-digital converters (ADCs). To provide more flexibility and to comply with the emerging communication standards, high-performance ADCs are required shown in Fig.1.1.

Fig.1.1. General Block Diagram Analog to Digital Conversion

Since analog-to-digital converters (ADCs) ultimately limit the performance of today's communication systems, high-speed, high- resolution, and power-aware ADCs are required in order to comply with new communication standards. This also leads to an increased demand for high-speed and high-resolution sampling systems in the measurement industry.

Present one possibility to overcome these performance limits is to use parallelism, i.e., to split the information of the analog input signal into several parallel channels, to convert them independently and finally to recombine them into one digital output signal. In theory, there are many ways to split the information of the input signal. In practice, only a few parallel multi-channel sampling structures have been further analyzed, where the time- interleaved structure is among the most promising ones for the future.

The idea of a time-interleaved ADC (TI-ADC) is that each channel in a system of M parallel channels alternately takes one sample, whereas the sampling frequency of one channel does not need to fulfil the Nyquist Criterion. However, when in the digital domain all samples merge into one sequence we obtain an overall sampling frequency that fulfils the Nyquist criterion. Thus, sampling with an ideal TI-ADC with M channels is equivalent to sampling with an ideal ADC with an M times higher sampling rate. The channels of a TI-ADC can be realized in different converter technologies to achieve for example high-rate and low-power ADCs or high-rate and high-resolution ADCs. Hence in this regard, a time-interleaved ADC (TI-ADC) shown in Fig.1.2 can be a reasonable solution.

Fig. 1.2. Four Channel Time-Interleaved ADC with frequency responses.

Results obtained from simulations of the proposed design are compared with experimental results of ALUs.

Ĥ0 (j Ω)

Ĥ1 (j Ω)

(2n+0)Ts

(2n+1)Ts

ADC1 ADC0

MUX x(t)

Ĥ1 (j Ω)

(2n+3)Ts

Digital O/P y(n)

fs=

Ĥ0 (j Ω)

(2n+2)Ts

ADC3

ADC4

Transfer Function Channel

Analog Input Signal

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II. MODELLING OF TI-ADC SYSTEM

This section discusses the operation of the time-interleaved ADC. The model presented serves as a foundation that allows the inclusion of time-varying errors due to differences between the sub-ADCs, as discussed in Sect. 2.2. The time-interleaved ADC, as shown in Fig. 2.1a, has an input x(t) and an output Y[n]. The sampling period of the time-interleaved ADC and the N sub-ADCs are Ts and Ts = N.Ts, respectively. The ith sub-ADC, where i = 0,....,N - 1, is strobed with clock ft(t), which

ideally has sampling edges at

[ ] ̂

( ) (2.1) Thus, the sampling edges of two consecutive clocks are offset by Ts, as in Fig. 2.1b, and the input signal is uniformly sampled. The output of the ith sub-ADC is ŷi[n],

where

̂[ ] ( [ ])

([ ] ) (2.2)

Fig. 2.1 (a) Time-interleaved ADC. (b) Sampling edges of sub-ADC clocks

The sub-ADC outputs ŷi[n] are multiplexed to create

y[n], such that

[ ] ̂ [ ] where i=n mod N (2.3) Setting yi[n] as the sub-ADC output ŷi[n] up sampled

by N results in

[ ] { ̂ [ ]

( )

This is simplified by defining

[ ] ∑ [ ] ( )

such that

[ ] ( ) [ ] ( )

Thus, the time-interleaved ADC output y[n] in (2.3) becomes

[ ] ∑ [ ] ( )

As expected, the output of the ideal time-interleaved ADC reduces to y[n]= x(nTs).

Frequency Domain Analysis:

To represent TI-ADC the discrete-time Fourier transform (DTFT) is used, discrete-time output y[n] and the sub-ADC output yi[n] in the frequency domain [6]. In general, the DTFT of a discrete-time input x[n] [7] is

Where X(f) is periodic with period 1. The inverse transform is

Sub-ADC Output:

The DTFT of the upsampled sub-ADC output yi[n] in (2.6) is

where x[n]= x(nTs). By property of the DTFT [7], Yi (f)

is equal to the convolution of the DTFTs of x[n] and δi [n]. The DTFT of the sampled input x[n] is X(f), whereas the DTFT of δi[n] [8] is

[image:2.595.67.289.362.657.2]

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This results in replicas at spacing’s of because of the sub sampling behaviour ofthe sub-ADCs. A phase-shift exists as a function of Yi(f), due to the exponential,

suchthat, even though the magnitude of Yi(f) is the same

for all the sub-ADCs, thephases are different.

Time-Interleaved ADC Output:

The DTFT of the time-interleaved ADC output y[n] in (2.7) is

and, using (2.12), can be written as

where M[k] is defined as

Thus

and the inverse DTFT of Y(f) is x[n], as expected.

Frequency Domain Analysis:

The ith sub-ADC output can be rewritten as

[image:3.595.332.551.158.359.2]

Where oiis the sub-ADC offset and hi(t) is a linear time-invariant function that is applicable to model both the sub-ADC gain and timing skew. It can also be applicable to model other effects, such as bandwidth mismatch [9], although this is not discussed here.

Fig. 2.2 Gain, offset, and timing skew in an N-channel time-interleaved ADC

The Effect of Time-Varying Errors:

Fig. 2.3 Effect of mismatch on sampled signal with N = 2. (a) With no mismatch. (b) With offset mismatch. (c) With gain mismatch. (d)

With timing skew

For example, gain is modelled with hi (t)= Gi .δ(t) and timing skew with hi(t)= δ (t- τi)/. When these effects are

included, the DTFT of yi[n] in (2.10) becomes

Where Di(f) is as in (2.11), and X^i(f)as the DTFT of hi (nTs)* x(nTs) such that

Simplifies Yi(f)into

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This is a generic setup for the errors in time-interleaved ADCs. As is seen in (2.24), the phases of the different sub-ADCs do not necessarily cancel out as they did in the ideal time-interleaved ADC because of Hi(f) which is no longer unity. The three cases of offset, gain and timing skew will individually be expanded on.

Fig. 2.6 Time-interleaved ADC output with offset mismatch

Effect of Offset Mismatch:

With offset mismatch, hi(t)=δ(t) such that Hi(f)=1, and oi not equal to 0. Therefore, Mh[k] in (2.24) simplifies to

(2.15), and

The resulting spectrum has tones spaced at 2fk/N , due to oi(f). These tones are not a function of the input signal,

[image:4.595.331.488.402.497.2]

and only depend on the size of the offsets and the number of sub-ADCs. For example, using the input spectrum of Fig. 2.2, the resulting output with an interleaving factor of four and with offset mismatch is as shown in Fig. 2.6.

Fig. 2.7 Time-interleaved ADC output with gain mismatch

Effect of Gain Mismatch:

With gain mismatch, hi(t)= Gi δ(t) such that Hi (f) = Gi, and Oi= 0. Therefore,

Where

If Gi=1 for all the sub-ADCs, then Mh[k] becomes

M[k], as previously defined. However, when the gains are not all identical, the replicas in the sub-ADC outputs do not necessarily cancel out. The magnitude of these residual replicas is a function of the sub-ADC gains, such that the gain errors effectively amplitude modulate the input signal. For example, Fig. 2.7 plots the resulting output DTFT for an ADC with gain mismatch and an interleaving factor of four, using the input signal of Fig. 2.2. As is expected non-zero replicas exist because of gain errors.

Impact of Offset:

With the assumptions that the gain and timing skew for all N sub-ADCs are identical such that, without loss of generality, Gi = 1 and τi= 0, the mean-square error in

(2.39) reduces to

Therefore, the SNR due to offset is

and the statistical bound on the variance of offset, using (2.44), is

Thus, the bound on offset is a function of the number of sub-ADCs N, the input signals power P, and the ADC resolution B. The bound on offset is unique when compared to that of both gain mismatch and timing skew since it is directly proportional to P. It is intuitive that ADCs with higher power input signals can cope with larger sub-ADC offsets. Furthermore, as shown in (2.47), higher resolution ADCs result in smaller bounds on offset mismatch, as does a higher interleaving factor, although the ADC resolution has a much larger effect on the bound. For example, if P = 0:5V2, B = 10, and N = 2, then σo≤

0.8mV.

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Impact of Gain:

With the assumptions that the offset and timing skew for all N sub-ADCs are identical such that, without loss of generality, oi = 0 and τi =0, the mean-square error in

(2.39) reduces to

Therefore, the SNR due to gain is

Note that the SNR due to gain mismatch is independent of the signal power, and only depends on the magnitude of the individual gains. The statistical bound on the variance of gain, using (2.44), is

This is almost identical to (2.47) in that it is inversely proportional to both the ADC resolution B and the interleaving factor N.

However, it does not depend on the signal power P or on any other signal information. For example, if N = 2 and B = 10, then σG ≤ 1.1%.

Ideal Filter:

In this example, white noise is passed through an ideal low pass filter with cut off frequency fcHz; the resulting

signal has an autocorrelation function of

Without loss of generality, we set τ0 = 0, which is the

timing skew of the first sub-ADC. This allows us to vary the timing skew τ1 of the second sub-ADC and plot the

theoretical value of (2.53) as a function of τ1 for different

values of fc. This theoretical SNR is compared to that obtained with Monte Carlo simulations in Fig. 2.12 for different values of fc. As is expected, the SNR increases for a given τ1 as fc decreases.

III. RELATED WORK

Time Interleaved ADC is the area of research for a long time few of them and recent works is listed below. Below table compares the method and their respective proposed approaches also given.

TABLE 1

PREVIOUS WORKS ON TI-ADC SYSTEM

S.No. Paper Title Year Objective Methodology Results

1

Digital Automatic Calibration Method for a Time-Interleaved

ADCs System used in Time-Domain EMI Measurement

Receiver

IE

EE

, 2012

To overcome this limitation and to extend the baseband of the

time-domain EMI receiver

A time interleaved sampling architecture is

introduced

Types of Error Before

calibration

After calibration

Gain and Offset

Mismatch 40dB 45dB

2

Adaptive Blind Background Calibration of

Polynomial-Represented Frequency Response Mismatches in a two Channel. Time Interleaved ADC

IE

EE

, 2011

To Compensate Frequency Response Mismatches including Gain timing & Bandwidth

mismatches

Filtered-X Least Mean Square (FxLMS) algorithm.

Types of Error _calibrationBefore _calibrationAfter

Frequency

Mismatch 32.6 dB 60.3 dB

Gain & Timing

Mismatch 36.3 dB 62.8 dB

3

A new DFT based Approach for Gain Mismatch Detection and

Correction in TI-ADC

IE

EE

, 2010

To correct and Detect gain mismatch between ADC

sub-channels in Time Interleaved ADC

Discrete Fourier Transform Technique

Signal Range Before

calibration

After calibration SFDR for gain

Mismatch 40 dB 72 dB

4

Correction of Mismatches in a Time-Interleaved

Analog-to-Digital converter in an Adaptively Equalized Digital

Communication Receiver

IE

EE

, 2009

To Overcome the errors caused by offset, gain,

sample time, and bandwidth mismatches

along TIADC

Least Mean Square (LMS) Adaptation

Algorithm.

Types of Error Before

calibration

After calibration

Gain only 21 dB 41.2 dB

Offset only 13.1 dB 41.8 dB

Bandwidth only 23.9 dB 40.6 dB

All errors present 10.6 dB 40.3 dB

5

Comprehensive Digital Correction of Mismatch Errors for a 400-Msamples/s

80-dB SFDR TI ADC

IE

EE

, 2005

It is a method to compensate frequency

response mismatches based on multirate theory

and least-squares filter

(FIR) filters designed by the

weighted least squares

Signal range Before

calibration

After calibration

[image:5.595.56.286.206.302.2] [image:5.595.52.563.462.757.2]

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IV. PROPOSED METHODOLOGY

This paper presents an adaptive technique for the blind calibration of the polynomial-represented frequency response mismatches in a four-channel TI-ADC. The contributions of the paper are the following:

1) Adaptive Calibration Structure:

We present an adaptive calibration structure that exploits the polynomial representation of frequency response mismatches for this purpose. It therefore extends the structure presented in [16], which can reconstruct the ideally sampled signal, but was not adaptable to general frequency response mismatches.

2) Blind Adaptive Background Calibration:

By combining the calibration structure with the spectral properties of slightly oversampled input signals, we can show how to utilize the filtered error least-mean square (FxLMS) algorithm to blindly identify frequency response mismatches, and, consequently, exploit the identified frequency response mismatches to remove the mismatch artefacts from the TI-ADC output signal.

3) FIR Filter Implementation:

[image:6.595.367.513.165.448.2]

In our proposed Methodology we would implement the FIR filter for noise filtration and gives the desire results.

Fig. 4.1 Functional Diagram of Proposed Methodology

[image:6.595.57.299.440.587.2]

The block diagram of Proposed Methedology shown below:

Fig. 4.2 Block Diagram of Proposed Methodology

[image:6.595.53.289.625.728.2]

The Flow Chart of Proposed Methodology shown below:

Fig. 4.3 Flow chart of execution of Simulation Model of Proposed Approach

V.SIMULATION RESULTS

The simulation of proposed methodology is implemented on MATLAB release R2011a version 7.12. The 4-Channel TI-ADC system has been designed in the matlab environment and we have considered all the four possible mismatches i.e. frequency, time, offset and gain. The simulations results has been shown in the graphs given below. Which is shown in the figure 5.1 onwards.

In Fig. 5.1 we have shown the analog signal given as an input to the Four Channel TI-ADC System and its magnitude spectrum. This magnitude has some unwanted frequency spurs called as quantization noise.

Start

Create Analog Signal of High Frequency approx 457 MHz

Initialize Environmental Variables for 4 channel TI ADC

Now Introduce Time, Frequency, Gain and Offset Mismatches

Apply Fx-LMS Algorithm For Mismatches Calibration

On the output of Fx-LMS algorithm Apply FIR – Band Pass Filtering

Display separate results for all the mismatches and combined effects

End

I/P Signal

Two Channel

TI-ADC

Fx-LMS _FIR

Filter

Mismatches

O/P Signal

Filtered Signal Calibrated

Signal Mismatched

Signal Ĥ0 (j Ω)

Ĥ1 (j Ω)

(2n+0)Ts

(2n+1)Ts

ADC1 ADC0

MUX x(t)

Ĥ1 (j Ω)

(2n+3)Ts

Digital O/P y(n)

fs=

Ĥ0 (j Ω)

(2n+2)Ts

ADC3

ADC4

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Fig. 5.1 (a) Input analog signal and (b) its magnitude spectrum

Fig. 5.2 Time mismatch in Input analog signal and calibrated output using Fx-LMS Algorithm

[image:7.595.333.552.142.315.2] [image:7.595.65.278.143.308.2]

In Fig. 5.2 the time mismatches has been introduced in the signal and then we applied the Fx-LMS algorithm which calibrate this mismatch to some extent than to minimize more this mismatch we have applied the FIR high pass filter and the filtered output is shown in Fig. 5.3, with the help of this filter application the mismatches as well as the quantization noise is also suppressed to some extent which is visible in the result of filter output, and SNR before and after calibration & filtering shown in Fig. 5.4.

[image:7.595.62.280.338.508.2]

Fig. 5.3 After applying the FIR filter on the Calibrated signal by FxLMS

Fig. 5.4 SNR before and after calibration & filtering

[image:7.595.329.553.465.634.2]

In Fig. 5.5 the offset mismatches has been introduced in the signal and then we applied the Fx-LMS algorithm which calibrate this mismatch to some extent than to minimize more this mismatch we have applied the FIR high pass filter and the filtered output is shown in Fig. 5.6, with the help of this filter application the mismatches as well as the quantization noise is also suppressed to some extent which is visible in the result of filter output, and SNR before and after calibration & filtering shown in Fig. 5.7.

Fig. 5.5 Offset mismatches in the input signal and calibrated output

Fig. 5.6 Filtered output of offset mis-matches

0 1 2 3 4 5 6

x 10-3 -1 -0.5 0 0.5 1 A m p lit u d e (a)

Time (s)

0 50 100 150 200 250 300 350 400 450 500

-150 -125 -100 -75 -50 -25 0 (b) Frequency (MHz) dB

0 100 200 300 400 500

-150 -130 -110 -90 -70 -50 -30 -10 Timing Mismatches Frequency (MHz) M a g n it u d e ( d B )

0 100 200 300 400 500

-180 -160 -140 -120 -100 -80 -60 -40 -20 0

Timining Mismatch After Calibration Using FxLMS Algorithm

Frequency (MHz) M a g n it u d e ( d B )

0 100 200 300 400 500

-150 -130 -110 -90 -70 -50 -30 -10

Timining Mismatch After Calibration using FxLMS Algorithm

0 100 200 300 400 500

-180 -160 -140 -120 -100 -80 -60 -40 -200 Frequency (MHz) M a g n it u d e ( d B )

Timing Mismatch After Highpass Filtering

Filtered Output

150 160 170 180 190 200

-50 0 50 100 Frequency (MHz) SN R (d B) (b)

SNR Before Calibration (Time Mismatch)

150 160 170 180 190 200

-10 -5 0 5 10 Frequency (MHz) SN R (d B) (b)

SNR After Calibration and Filtering(Time Mismatch)

0 50 100 150 200 250 300 350 400 450 500

-180 -160 -140 -120 -100 -80 -60 -40 -20 0 Before Calibration Frequency (MHz) M a g n it u d e ( d B )

0 50 100 150 200 250 300 350 400 450 500

-180 -160 -140 -120 -100 -80 -60 -40 -20 0

After Calibration Using FxLMS Algorithm

0 100 200 300 400 500

-180 -160 -140 -120 -100 -80 -60 -40 -20 0

Offset Mismatch after Calibration using FxLMS Algorithm

0 100 200 300 400 500

-180 -160 -140 -120 -100 -80 -60 -40 -20 0 Frequency (MHz) M a g n it u d e ( d B )

Offset mismatch after Highpass Filter

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In Fig. 5.8 the Gain mismatches has been introduced in the signal and then we applied the Fx-LMS algorithm which calibrate this mismatch to some extent than to minimize more this mismatch we have applied the FIR high pass filter and the filtered output is shown in Fig. 5.9.

Fig. 5.8 Gain mismatches in the input signal and calibrated output

Fig. 5.9 Filtered output of Gain mis-matches

With the help of this filter application the mismatches as well as the quantization noise is also suppressed to some extent which is visible in the result of filter output, and SNR before and after calibration & filtering shown in Fig. 5.10.

[image:8.595.60.284.411.671.2] [image:8.595.332.553.464.690.2]

In Fig. 5.11 the Frequency mismatches has been introduced in the signal and then we applied the Fx-LMS algorithm which calibrate this mismatch to some extent than to minimize more this mismatch we have applied the FIR high pass filter and the filtered output is shown in Fig. 5.12, with the help of this filter application the mismatches as well as the quantization noise is also suppressed to some extent which is visible in the result of filter output, and SNR before and after calibration & filtering shown in Fig. 5.13

Fig. 5.11 Frequency mismatches in the input signal and calibrated output

Fig. 5.12 Filtered output of Frequency mis-matches

150 160 170 180 190 200

-20 0 20 40 60 Frequency (MHz) SN R (d B) (b)

SNR Before Calibration (Offset Mismatch)

150 160 170 180 190 200

SNR After Calibration and Filtering (Offset Mismatch)

0 50 100 150 200 250 300 350 400 450 500

-180 -160 -140 -120 -100 -80 -60 -40 -20 0

0 50 100 150 200 250 300 350 400 450 500

-180 -160 -140 -120 -100 -80 -60 -40 -20 0

Output after Calibration using FxLMS Algorithm

0 50 100 150 200 250 300 350 400 450 500

Output of Highpass Filter

Filtered Output

150 160 170 180 190 200

30 40 50 60 70 Frequency (MHz) SN R (d B) (b)

SNR Before Calibration (Gain Mismatch)

150 160 170 180 190 200

SNR After Calibration and Filtering (Gain Mismatch)

0 50 100 150 200 250 300 350 400 450 500

-180 -160 -140 -120 -100 -80 -60 -40 -20 0

0 50 100 150 200 250 300 350 400 450 500

-180 -160 -140 -120 -100 -80 -60 -40 -20 0

0 50 100 150 200 250 300 350 400 450 500

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In Fig. 5.14 the All mismatches (Time, Gain, Frequency and Offset) have been introduced in the signal.

Fig. 5.14 All mismatches in the input signal and calibrated output

[image:9.595.64.283.373.545.2]

and then we applied the Fx-LMS algorithm which calibrate this mismatch to some extent than to minimize more this mismatch we have applied the FIR high pass filter and the filtered output is shown in Fig. 5.15, with the help of this filter application the mismatches as well as the quantization noise is also suppressed to some extent which is visible in the result of filter output, and SNR before and after calibration & filtering shown in Fig. 5.16.

Fig. 5.15 Filtered output of All mis-matches

Fig. 5.16 SNR before and after calibration & filtering Table 2

SFDR Performance

Type of Mismatch

SFDR Before Calibration

SFDR After Calibration Frequency Mismatch 128.4089 dB 138.6235 dB

Offset Mismatch 48.93 dB 143.5921 dB

Gain Mismatch 47.1031 dB 146.8517 dB

Time Mismatch 17.2459 dB 145.4931 dB

All Mismatches 17.2323 dB 145.5568 dB

Table 2 shows the SFDR performance before and after calibration and filtering with respect to frequency, gain, offset, time and all mismatches.

VI. CONCLUSIONS

In this paper, we have implemented FIR high pass filter for a to calibrate the frequency, time, offset and gain mismatches in a four-channel TI-ADC. Here we have designed a simulated system model of a four-channel TI-ADC with mismatches, where the all the mismatches are represented. Firstly we have implemented a blind calibration structure i.e. Filtered-Least Mean Square(FxLMS) algorithm to identify the unknown coefficients of the which can calibrate the signals iteratively in the presence of all possible mismatches. after calibration the highpass FIR filter has been applied to minimize the mismatch affects on signal. The simulation results have demonstrated that with this calibration structure of proposed methodology we can achieve a considerable amount of reduction in mismatches.

150 160 170 180 190 200

25.568 25.57 25.572 25.574 25.576

Frequency (MHz)

SN

R

(d

B)

(b)

SNR Before Calibration (Frequency Mismatch)

150 160 170 180 190 200

-50 0 50 100 150

Frequency (MHz)

SN

R

(d

B)

(b)

SNR After Calibration and Filtering (Frequency Mismatch)

0 50 100 150 200 250 300 350 400 450 500

-180 -160 -140 -120 -100 -80 -60 -40 -20 0

Before Calibration

Frequency (MHz)

M

a

g

n

it

u

d

e

(

d

B

)

0 50 100 150 200 250 300 350 400 450 500

-180 -160 -140 -120 -100 -80 -60 -40 -20 0

Frequency (MHz)

M

a

g

n

it

u

d

e

(

d

B

)

0 50 100 150 200 250 300 350 400 450 500

-180 -160 -140 -120 -100 -80 -60 -40 -20 0

Frequency (MHz)

M

a

g

n

it

u

d

e

(

d

B

)

0 50 100 150 200 250 300 350 400 450 500

-180 -160 -140 -120 -100 -80 -60 -40 -20 0

Frequency (MHz)

M

a

g

n

it

u

d

e

(

d

B

)

Filtered Output

150 160 170 180 190 200

-50 0 50 100

Frequency (MHz)

SN

R

(d

B)

SNR Before Calibration (All Mismatch)

Before Calibration

150 160 170 180 190 200

-10 -5 0 5 10

After Filtering

Frequency (MHz)

SN

R

(d

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Author’s Profile

Vandana Ben Patel is a research scholar at Sagar Institute of