This paragraph describes three different types of control feedback. First, the proportional control is simulated. Secondly, a proportional-derivative control is evaluated in order to increase the damping of the control signal. Finally, an integral factor is added to eliminate the steady state error. The consecutive values of the input power are: -30, -20 and -10 dBm.
P-control
The P-control AGC follows the approach as proposed by Jansen [3]. The proportional transfer function Dpis:
(3.9)
The parameter settings of the Bulk_SOA model are shown in Table B.2 and the control-loop settings are presented in Table 3.1.
Table3.1Parameters of P-control simulation of of theAGewithout data.
System Symbol Parameter Value Unit
Global TimeWindow 51.2 ns
SampleModeBandwidth 640 GHz
SOAB I Bias current 50 mA
Control loop Vre, Reference Voltage 1060 mV
I~W
Bandwidth loop filter 100 IMHZ Proportional gain 10 AN Slewing rate 5.108 'IV/sFigure 3.5 shows different signals of the P-control AGC. The drive current plot shows the effect of the transient time of the SOAs. T
=
0 s, the initial carrier density is very low (1.0x 10241/m\
and from equation 3.6 the junction voltage is also low resulting in a negative error voltageVj -Vref.Therefore, the drive current is zero in the first 7 ns.Chapter3Simulations 3.4 Results
Power[dem] output SOA 2 33r - : - - - -10
Figure 3.5 Proportional control signals;
(a) input signal; (b) error voltage; (c) drive current of SOA 1;(d) output power of SOA 2.
After the transient time, the AGC reaches a steady control situation for the -30 dBm input power. The drive current of SOA 1 is 30 mA and using equation 3.9 and K=10 the error voltage is 3 mV.
After 69 ns, the input power into SOA 1 changes to -20 dBm and this results in an instantaneously power step at the output of SOA 2. The increased photon density in SOA 2 saturates this amplifier and therefore the junction voltage decreases due to the lower carrier density. Because of the saturation effect, the output power of the AGC has become lower than the desired value and the drive current is increased to reach a steady output power. The drive current stabilises at 22.5 mA and the error voltage is 2.25 mV.
The outputofthe SOA 2 for a -30 dBm input has more noise than for the -20 dBm input. Because the automatic gain control has to amplify the -30 dBm more, also a larger noise contribution will be added.
Different input powers result in different error voltages and consequently different output powers for the AGC. Figure 3.5.d shows indeed a 5 dB difference in the final value between the -30 and -20 dBm input power.
For t=137 ns the input power increases to -10 dBm and again a step in the output power occurs. For this input power the control signal oscillates. The proportional gain is too high for this input power.
PD-control
In order to improve stability, a proportional-derivative (PO) control is introduced with a transfer function DpD :
(3.10)
\l\lhere "Cd [s] is the derivative time constant. The derivative feedback increases the damping and improves the stability of the system. Table 3.2 shows the parameters of this simulation, which are the
Chapter3Simulations 3.4Resuffs
same as the parameters in the proportional control simulation except for the extra derivative component.
Table3.2 Parameters of PO-control simulation of of the AGC without data.
System Symbol Parameter Value Unit
Global TimeWindow 51.2 ns
SampleModeBandwidth 640 GHz
SOAB I Bias current 50 mA
Control loop Vref Reference voltage 1060 mV
BW Bandwidth loop filter 100 MHz
K Proportional gain 10 AN
'rd Derivative time constant 10.10-9 s
S, Slewing rate 5.108 Vis
The control signals in Figure 3.6 show more damping compared to the P-control response. A PD-control still has the disadvantage of a nonzero steady-state error.
b.
100 Time Ins] 205 0 100 Time Ins] 205 -25
Power[clBm] output SOA 2 33 . - - - , 1 0
Figure 3.6 PO-control signals;
(a) input signal; (b) error voltage; (c) drive currentof SOA 1;(d) output powerof SOA 2.
Figure 3.7 shows the individual contributions of the proportional and derivative components to the total control signal of the AGC. The derivative component increases the transient speed of the control signal and its contribution decreases for the steady state.
Chapter3Simulations 3.4 Results
Proportional and derivative contribution to the drive curent [rnA]
Proportional'
Figure 3.7 Proportional and derivative contributions to the PO-control signal.
PID-control
The problem of the steady-state error can be solved using a proportional-integral-derivative (PIO) control. The main advantage of combining the PO-control with an extra integral control is the reduction of the steady state error Vj -Vref .The control transfer function OPID is:
0P/O(s)= K·(1+_1_+S'dJ
S'I
(3.11 )
VVhere 'd [s] and 'I [s] are the derivative and the integral time constant, respectively. The proportional feedback increases the speed of the response; the integral component eliminates the steady-state error whereas the derivative part can damp the dynamic response.
Table 3.3shows the parameters of the PIO simulation. The input signal is alternated from -30to-20 and -10 dBm to evaluate the effect of a step in average power on the AGC behaviour.
Table 3.3 Parameters of PIO-control simulation of of the A GC without data
System Symbol Parameter Value Unit
Global TimeWindow 102.4 ns
SampleModeBandwidth 640 GHz
SOAB I Bias current 50 mA
Control loop Vref Reference voltage 1060 mV
BW Bandwidth loop filter 100 MHz
K Proportional gain 10 AN
'td Derivative time constant 10.10-$ s
'tl Integral time constant 0.5,10·g s
S, Slewing rate 5.108 VIs
Chapter3Simulations
a.
Power [dBm] Input signal -19.7
-25
b.
uj-uref [mY]
4.3 . - - - ,
2
oI---"'h'h_--tf\-tv---!
-2
3.4 Results
-30.2 -5
0 100 TimeIns] 205 0 100 TimeIns) 205
C. d.
driue current [rnA) Power (dBml output SOA 2
48 7
40
0 30
20 -10
10
-1 ·25
0 100 TimeIns) 205 0 100 TimeIns] 205
Figure 3.8 PID-control signals;
(a) input signal; (b) error voltage; (c) drive current of SOA 1;(d) output power of SOA 2.
The effect of the integral component on the AGC response is as expected. The error voltage in Figure 3.8b fades out resulting in a zero error voltage of the AGC control signal. Figure 3.9 shows the proportional, integral and derivative contributions to the total control current. The integral component slows the response but it also eliminates the error voltage, as the proportional line decreases to zero.
The derivative component is only present at the points where the input power changes.
Chapter3Simulations 3.4 Results
Proportional, integral, derivative contribution to the drive current [rnA]
51 , - - - ,
Figure 3.9 Proportional, derivative and integral contributions to the total control signal.