3. Skew measurement in coherent optical transmitter based on image spectrum analyzing
3.3. Transmitter IQ skew measurement based on image spectrum analyzing
3.3.1. Principle and theoretical derivation of image spectrum analyzing
Fig 3. 4 Impairment model including transmitter IQ skew in the coherent optical transmitter
Fig 3. 5 Image signal spectrum variation with nonzero transmitter IQ skew when sending single sideband (SSB) signal
There are several impairments in the coherent optical transmitter, which cause significant penalty and require accurate measurement and calibration. The general model of these impairments is shown in Fig 3. 4, which includes the amplitude imbalance
A
, IQ skew
and the bias phase error
. The bias phase error is the bias deviation to 90 degree for parent Mach-Zehnder structure whose optimum value is zero. The output optical field of the modulator can be given by( )
( ) sin( ( ) ) sin( )
2 2
i Q
I
V t
E t V t ie A
V V
Eq 3. 1Single sideband (SSB) comb signal which only has either positive or negative frequency component is proposed to be as the test signal to detect the image spectral components containing the IQ skew information. And the image spectrum variation with nonzero transmitter IQ skew is illustrated in Fig 3. 5. The I and Q signal input to the modulator of the SSB signal can be expressed by
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( ) cos(2 )sin( ( )) 2 ( ) sin(2 )sin( ( ))
2
I
I n n n
n
I
Q n n n
n
V t A f t V t
V V t A f t V t
V
Eq 3. 2
where
A
n,f
n and
n are the amplitude, frequency and phase of the nth component of comb signal, respectively. The phase {
n} should be carefully designed to optimize the peak-average power ratio (PAPR) of the signal waveform in order to use the DAC swing efficiently.Substituting Eq 3.2 to Eq 3.1 and considering small bias deviation and fundamental component of Bessel function extension for triangle function, the output optical field is expressed by
(2 ) ( -2 ) (2 ) ( 2 )
1
1 1
( ) ( ){ (1 ) (1 )}
2
n n n n n n
j f t j f j f t j f
n n
E t J A e e e e
V A A
Eq 3. 3 Where J1(·) is the 1st order Bessel function of the first kind. The first term in bracket is the main signal at frequency
f
n, and the second term is the image signal at frequency f
n.By sending the SSB comb signals with positive and negative frequency separately and using Eq 3.3, the image-to-main signal ratio (IMSR) can be measured individually at each frequency, and expressed by
2 2
( ) 1 2 cos( 2 )
( )
( ) 1 2 cos( 2 )
image n n
n
main n n
P f A A f
IMSR f
P f A A f
Eq 3. 4As in Eq 3.4, the image spectrum shape is fully determined by the IQ skew value, which would be flat when transmitter IQ skew
is zero. Reorganizing Eq 3.4 and with pre-measured amplitude imbalance valueA
, the transmitter IQ skew can be calculated from the image spectrum by1 1 2 1 ImageSpec( )
arccos( )
2 2 1 ImageSpec( )
A f
f A f
Eq 3. 5
Alternatively, transmitter IQ skew can be calculated from the IQ phase, which includes transmitter IQ skew and bias phase error and defined by
（
n） （
n）
IQphase or
Eq 3. 6 which could be measured and calculated from the IMSR by Eq 3.4. The calculation method is shownin Fig 3. 6. When bias phase error is zero, first is to reverse the IQ phase of negative frequency components, and then the slope of the linear fitting curve of IQ phase versus frequency is used to calculate the transmitter IQ skew by
slope
2
Eq 3. 7When bias phase error is nonzero, first is to find the larger one between the IQ phase
summation of positive and negative frequency components. If positive frequency part is larger, the slope of the linear fitting curve of IQ phase versus positive frequency is used to calculate the transmitter IQ skew by Eq 3.7. If negative frequency part is larger, the slope of the linear fitting curve of IQ phase versus negative frequency is used to calculate the transmitter IQ skew by Eq 3.7.
Fig 3. 6 The method to calculate transmitter IQ skew from IQ phase
Obviously, the proposed transmitter IQ skew measurement method can measure the absolute value of IQ skew without the sign. To judge the sign of current IQ skew, another redundant transmitter IQ skew value could be measured after adjusting the digital delay by a known value e.g.
+1ps. If the measured absolute value of the second IQ skew is 1ps larger than the first one before adjustment, the sign of the first measured IQ skew is positive. Otherwise, the sign is negative.
3.3.2. Experiment setup to verify the transmitter IQ skew measurement method
Fig 3. 7 Experiment setup to verify the transmitter IQ skew measurement method
Experiment setup to verify the proposed transmitter IQ skew measurement method is shown in Fig 3. 7. 64Gsps DAC generated the SSB comb signals in range of 1~25GHz with 2GHz spacing.
Amplitude response of the transmitter was pre-equalized by the existing methods. Initial phases of SSB comb signal are designed to make the waveform PAPR in range of 4~6.25. The indium phosphide optical modulator with bandwidth 30GHz and π phase shift voltage of 2.5V was used to modulate the electrical signals. The original transmitter IQ skew could be from DAC, driver,
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modulator and the connection cables. Light source was a 1546.5nm continuous wave laser with 13dBm output power. An optical spectrum analyzer (OSA) with resolution bandwidth of 150MHz collected the main and image signal spectrum.
Fig 3. 8 Measured main signal and image signal spectrum with transmitter IQ skew 5.65ps One measured main signal and image signal spectra with the transmitter IQ skew is shown in Fig 3. 8 as an example. The dash line marks the wavelength of optical carrier. Fig 3. 8 a) shows the image spectrum with negative frequency components and Fig 3. 8 b) shows the image spectrum with positive frequency components, after these optical spectra move to the base frequency by subtracting the carrier frequency. The image spectrum shape is determined by the transmitter IQ skew as expressed in Eq 3.4. According to the equations in the previous sections, the transmitter IQ skew in this case is measured to be +5.65ps.