Abstract:
Circuits and methods for automatically controlling lightwave emitters are provided. A control system is provided that includes a variable gain circuit for automatically adjusting the gain of a control signal with respect to a feedback signal, a modulation signal, and a reference signal. This allows the optical output of the lightwave emitter to remain substantially constant despite changes in transfer ratio due to aging or temperature variations. Furthermore, in some embodiments, a user may select the overall gain of the system to optimize response time, bandwidth, or steady-state accuracy.

Description:
BACKGROUND OF THE INVENTION 
   This invention relates to automatic power control of light sources. More particularly, this invention relates to gain normalization and automatic power control of modulated light sources. 
   Recently, there has been a dramatic increase in the number of technologies that are based on the transmission of lightwave signals. Some popular examples of these technologies include data retrieval systems such as DVDs, data transfer systems such as fiber optics, and data acquisition systems such as bar code scanners. Generally speaking, lightwave systems are desirable because they take advantage of the unique properties of light such as extended bandwidth, the ability to propagate long distances with little loss, and resistance to electro-magnetic interference (EMI). 
   Lightwave technology has revolutionized the transmission of electronic information. For example, fiber optic communications systems that use semiconductor lasers can attain data rates far in excess of that normally found in copper wire systems. Because the light intensity of a semiconductor laser is usually linearly proportional to an injected current, and the current in a photodetector is linearly proportional to incident optical intensity, data may transmitted as a modulation of the optical intensity. Such a lightwave system is analogous to a linear electrical link where current or voltage translates linearly into optical intensity. High speed semiconductor lasers and photodetectors enable intensity-modulation bandwidths greater than 10 GHz, allowing the development of a wide variety of radio and microwave frequency applications. 
   Converting microwaves into intensity-modulated light allows the use of optical fiber for transmission in place of bulky inflexible coaxial cable or microwave waveguide. Because signal attenuation in optical fiber is much less that of cable or waveguide, entirely new applications and architectures are possible. In addition, optical signals are usually tightly confined to the core of single-mode fiber, where it is immune to EMI, cross talk, or spectral regulatory control. 
   To achieve these advantages, several limitations must be overcome. The conversion of current to light intensity must be substantially linear. Several nonlinear mechanisms must be avoided by proper laser design or by the use of various linearization techniques. 
   An example of a conventional lightwave transmission system  10  with automatic power control is shown in  FIG. 1 . Transmission system  10  includes a lightwave emitter  110 , a lightwave detector  120 , a summing node  130 , a reference signal  140 , a fixed gain circuit  20 , a modulator circuit  160 , and an optical transmission medium  170 . 
   In operation, a drive signal I D  is applied to lightwave emitter  110  so that emitter  110  produces optical output signal  115 . Optical output signal  115  is the principal output signal of circuit  10  which may be used to as optical data. As shown, principal signal  115  is applied to an optical transmission medium  170  for conveying the optical information. Another optical signal, monitor signal  116 , is also generated. Signal  116  may be created directly by lightwave emitter  110  or by sampling a portion of principal output signal  115 . Monitor signal  116  is applied to lightwave detector  120  to monitor the power of principal signal  115 . This is accomplished by generating a feedback signal I FB  that is representative of monitor signal  116 . Principal signal  115  and monitor signal  116  are usually proportional to one another so the feedback signal I FB  is proportionally related to principal signal  115 . 
   As shown in  FIG. 1 , both feedback signal I FB  and reference signal  140  (I REF ) are coupled to summing node  130 . Summing node  130  compares the feedback signal and the reference signal in order to produce a control signal I C  that is proportional to the difference of these signals (sometimes referred to as an error signal). Fixed gain circuit  20 , which is typically an integrator, receives control signal I c  and produces a bias signal I B  in order to maintain emitter  110  at a power level that allows effective modulation. Bias signal I B  is subsequently combined with modulation signal I M , which includes modulated information, to produce a drive signal I D  that controls the output of lightwave emitter  110 . In this way, the optical output of lightwave emitter  110  provides modulated optical communication signals to transmission medium  170 . 
   When drive signal I D  is initially applied to lightwave emitter  110 , system  10  experiences wide variations in operating parameters. Three parameters of particular concern to circuit designers are the threshold level and slope efficiency of emitter  110  and the sensitivity of detector  120 . 
   The threshold level of emitter  110  is generally defined as the magnitude of the drive signal I D  required to produce a desired minimum light level. The slope efficiency of emitter  110  is generally defined as the derivative of optical output signal  115  with respect to the input signal (I D ) when the input signal is above the threshold level. The sensitivity of detector  120  is generally defined as the ratio of the average value of the output signal (in this case the average value I FB ) to the average optical output power (in this case, the average value of optical output signal  115 ). 
   The threshold level is indicative of the level above which lightwave emitter  110  generates a useful optical output signal. Maintaining emitter  110  above this threshold level is generally desirable in optical transmission systems because it reduces the response time of emitter  110  to drive signal I D , minimizes the amplitude of I M  needed to produce the required optical modulation, and reduces duty cycle distortion. 
   The slope efficiency is representative of the amount of light produced by emitter  110  per unit drive signal I D . The value the slope efficiency directly affects the amplitude of the modulation signal I M  needed to produce the necessary optical modulation. 
   Initially, it is necessary to compensate for variations in the threshold level and slope efficiency of light emitter  110  and for variations in sensitivity of detector  120 . This is usually accomplished during the final assembly of transmission system  10  by selecting appropriate values for the amplitude of modulation signal IM and reference signal  140 . Typically, reference signal  140  is adjusted until the average optical power produced by lightwave emitter  110  conforms to a given communications standard such as one promulgated by the IEEE (e.g., ETHERNET). Similarly, the amplitude of modulation signal I M  is adjusted until the extinction ratio (i.e., the ratio between maximum instantaneous optical output power and minimum instantaneous optical output power) of optical output signal  115  is sufficiently high to conform with a given communication standard. 
   Over time and with changes in temperature, variations in the threshold level and slope efficiency cause the average power of optical output signal  115  to change. Summing node  130  senses this change through a corresponding change in feedback signal I FB  and modifies control signal I C . This causes a change in bias signal I B  to approximately correct for the change in optical output power. In this way, transmission system  10  maintains the average optical output power of lightwave emitter  110  approximately constant. 
   In addition to changes in average optical output power, a change in slope efficiency also adversely affects extinction ratio. This occurs because the change in slope efficiency changes the modulation amplitude of the optical output signal. This problem is commonly solved in system  10  by adjusting the amplitude of modulation signal I M  to maintain the modulation amplitude of optical output signal  115  substantially constant. 
   One problem with system  10 , however, is that variations in transfer ratio (i.e., the product of slope efficiency and detector sensitivity) reduce its ability to maintain the power of optical output signal  115  constant. In general, the accuracy with which any feedback control system, such as system  10 , can maintain its output in proportion to its input is limited by its loop gain. High loop gain is required for high accuracy, but excessive loop gain causes stability problems. If the loop gain is too low, however, large errors will be encountered in controlling average optical power. Because the loop gain in system  10  is dependent on the transfer ratio, the accuracy and stability of system  10  varies as transfer ratio varies. Thus, as transfer ratio decreases, system accuracy is sacrificed, and when transfer ratio increases, stability is compromised. 
   System  10  experiences a decrease in transfer ratio due to initial manufacturing tolerances of emitter  110  and detector  120  and to drift in emitter  110 . This causes several problems. Foremost among these is a decrease in system bandwidth which results in an undesirably long settling time when emitter  110  is turned on. If settling time is excessive, it takes too long to turn on and stabilize emitter  110 . However, if bandwidth is too large, the servo loop (i.e., the circuitry that controls emitter  110 ) will attenuate low frequency content in the communications signal. Thus, such an overlap is undesirable. 
   To deal with these well known performance limitations, international standard agencies such as the IEEE have adopted communication protocols that allow for very long settling times and attempt to minimize the overlap problem by requiring the use of high overhead encoding schemes such as 8B10B. Such long settling times however, make burst transmissions, which save electrical power and improve eye safety, virtually impossible. Moreover, this solution prevents accurate data transfer during the start up period and significantly reduces overall data rates. 
   Thus, in view of the foregoing, it would desirable to provide a system and method for gain normalization and automatic power control for modulated light sources that overcomes the above-described and other deficiencies found in conventional systems. 
   SUMMARY OF THE INVENTION 
   It is therefore an object of the present invention to provide circuits and methods for improving control of modulated light sources. 
   This and other objects of the present invention are accomplished in accordance with the principles of the present invention by providing circuits and methods automatically controlling lightwave emitters. A control system is provided that includes a variable gain circuit for automatically adjusting the gain of a control signal with respect to a feedback signal, a modulation signal, and a reference signal. This allows the optical output of the lightwave emitter to remain substantially constant despite changes in transfer ratio due to aging or temperature variations. Furthermore, in some embodiments, a user may select the overall gain of the system to optimize response time, bandwidth, or steady-state accuracy. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The above and other objects and advantages of the present invention will be apparent upon consideration of the following detailed description, taken in conjunction with the accompanying drawings, in which like reference characters refer to like parts throughout, and in which: 
       FIG. 1  is a block diagram of a conventional lightwave transmission system with automatic power control. 
       FIG. 2  is a block diagram of a lightwave transmission system with automatic power control constructed in accordance with the principles of the present invention. 
       FIG. 3  is graph illustrating how the response time of the system shown in  FIG. 2  is affected by loop gain when a step change is applied to the reference signal. 
       FIG. 4  is a frequency plot of three possible response times of the system shown in  FIG. 2  compared with the spectrum of a modulation signal. 
       FIG. 5  is one possible alternate embodiment of the system shown in  FIG. 2 . 
       FIG. 6  is another possible alternate embodiment of the system shown in  FIG. 2 . 
       FIG. 7  is schematic of an analog embodiment of the system shown in  FIG. 6 . 
       FIG. 8  is schematic of an digital embodiment of the system shown in  FIG. 6 . 
       FIG. 9  is schematic of a portion of the digital embodiment shown in  FIG. 8 . 
       FIG. 10  is a diagram defining specific levels of current relevant to biasing and modulating a lightwave emitter. 
   

   DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   A gain normalization system  100  constructed in accordance with the principles of the present invention is shown in  FIG. 2 . As in  FIG. 1  gain normalization system  100  includes a lightwave emitter  110 , a lightwave detector  120 , a summing node  130 , a reference signal  140 , a modulator circuit  160 , and optionally, may be coupled to optical transmission medium  170 . 
   Lightwave emitter  110  may be any suitable controlled lightwave emitting source such as a laser, a laser diode, a vertical cavity surface emitting laser (VCSEL), an edge emitting laser, a light emitting diode (LED), etc. Lightwave detector  120  may be any detector suitable for detecting light such as a photodiode, a phototransistor, a photoelectric detector, a charge coupled device (CCD), etc. 
   Gain normalization system  100  has been improved as compared to the system shown in  FIG. 1 , however, by replacing fixed gain circuit  20  with variable gain circuit  150 . As can be seen, circuit  150  is coupled to modulator  160  and reference signal I REF . This arrangement allows the gain of circuit  150  to be varied with respect to the amplitude of modulation signal I M  and with respect to reference signal I REF . Two important benefits are realized by allowing the gain of circuit  150  to be varied. The first is that the loop gain of system  100  is no longer dependent on its transfer ratio. The second is that the loop gain may be set to a predetermined value that remains constant despite variations in transfer ratio. 
   To illustrate the benefit of setting and maintaining the loop gain to a predetermined constant value, the effect of the loop gain can be analyzed. Referring to  FIG. 2 , the loop gain is defined as the total small signal gain in the control loop, or
 
 A=dI   FB   /dI   C   =G ( s )* dI   FB   /dI   B   (1)
 
where s is the Laplace variable and G(s) is the Laplace transform of variable gain circuit  150 .
 
   It is well known from elementary control system theory that for infinite loop gain, I C= 0, I FB =I REF , and therefore
 
 P   115 =( I   FB /γ)= I   REF /γ  (2)
 
where γ is the detector sensitivity or
 
γ= I   FB   /P   115   (3)
 
It can also be shown from elementary control theory that for finite loop gain
 
 P   115   =I   REF /γ*[A/(1 +A )]  (4)
 
If the variable gain circuit  150  is an integrator, as is commonly the case, the loop gain of the system  100  may be expressed as
 
 A=A ( s )= A   0 /( s*τ)   (5)
 
where A(s) is the Laplace transform of the loop gain. Combining equations 4 and 5 the optical output signal power can be written as
 
 P   115 =( I   REF /γ)/(1 +s*τ/A   0 )  (6)
 
Equation 6 represents a single-pole low pass filter with an effective time constant of
 
τ O   =τ/A   O   (7)
 
and 3 dB bandwidth
 
ω O=1 /τ O   =A   O /τ  (8)
 
   If Ao in equation 2 is a user selectable design parameter and may be chosen as a constant, then the effective time constant to and the 3 dB bandwidth ω o  are also user selectable constants. This allows the system designer to set these parameters to certain values based on design requirements. 
     FIG. 3  is a graph that illustrates how response time is affected by loop gain when a step change is applied to the reference signal (shown in  FIG. 3  as solid line  174 , I REF (t)). This closely parallels the behavior of system  100  when it is turned on. Because Ao is a selectable design parameter, a designer may choose a specific gain value for system  100  to obtain a specific response time. For example, a designer may choose Ao to be relatively large in order to obtain a faster response time. This is illustrated by dotted line  172 . If slower response times are desired, smaller values of Ao may be chosen to obtain the response times represented by solid line  171  and dotted line  173 . In this way, component manufacturers may select gain values specific to each component so that response times for a particular component type are substantially constant. Thus, one advantage of the present invention is that it permits the production of multiple systems  100  that have substantially the same response time. This is a dramatic improvement over prior art techniques that select a nominal gain to obtain a range of response times that in the worst case fall within the upper and lower bound allowed by the communication protocol. 
   The ability to accurately set the response time of system  100  has important consequences in the frequency domain.  FIG. 4  is a frequency plot of three system response times compared with the spectrum of modulation signal I M . In  FIG. 4 , solid line  181  and dotted lines  182  and  183  represent frequency response plots that correspond to the system responses shown in  FIG. 3 . For example, dotted line  182  is a frequency response plot of the response time represented by dotted line  172 , and solid line  181  is a frequency response plot of the response time represented by solid line  171 , etc. 
   As can be seen from  FIG. 4 , selecting a fast response time results in the frequency characteristic depicted by dotted line  182 , whereas selecting slower response times results in the frequency characteristics depicted by solid line  181  and dotted line  183 . Because the system designer can control response time, the frequency response profile of system  100  is also controllable. This enables the designer to tailor the frequency response profile of system  100  to meet operational requirements. In particular, the bandwidth of system  100  should not be too low or the system would fail to meet settling time requirements at startup. Also, the bandwidth of system  100  should not overlap the low frequency portion of the spectrum of the modulation signal I M , shown as solid line  184 , or it would suppress the low frequency content of the modulation signal. 
   In a digital optical communications system, for example, it may be desirable to use a low-overhead data encoding scheme that allows long consecutive strings of high or low signal levels and has a relatively high portion of its total energy concentrated at low frequencies. In this case, a slower system response time (i.e., lower bandwidth) is preferred to prevent the control loop bandwidth from overlapping with the modulation signal spectrum. 
   In other applications, however, such as short-duration, high speed communications, or in power sensitive applications where system  100  is turned on and off frequently, it is generally desirable to have system  100  respond as fast as possible in order to properly bias emitter  100  for data transmission. Furthermore, the more rapidly system  100  can establish stable bias of the light emitter the sooner the system can enable any safety fault mechanisms. However, it is well known that if the response time of system  100  is too fast, distortion results in the modulation portion of optical output signal  115 . 
     FIG. 2  is somewhat similar to the prior art system in  FIG. 1  in its overall operation but contains a different set of signal processing functions within variable gain circuit  150 . Within circuit  150  the I REF  and I M  signals are used to normalize the overall loop gain to a constant value independent of the characteristics of lightwave emitter  110  and lightwave detector  120 . The signal I M  entering variable gain circuit  150  is generally the peak-to-peak value of the modulation signal I M  that is delivered to light emitter  110 . Circuit block  210  divides signal I C  by I REF  as required by equation 26 below. Startup aid  240  ensures that the input to multiplier  220  is above zero and therefore that the control loop gain is above zero. Startup aid  240  may be omitted if I M  is above zero during setup and normal operation. Amplifier block  230  may be implemented as a pure integrator, as a proportional-integral-derivative (PID) circuit, or any other suitable arrangement. In certain embodiments, the gain of circuit  150  may be bounded such that it does not drop below a minimum value or exceed a maximum value. This may done to ensure stability and response time. 
   Startup aid  240  can be implemented in a variety of ways. Three examples of algorithms for implementing the startup aid  240  are as follows:
         1: S=I M +C   2: S=max(I M , C)   3: S=if I M &gt;0 then I MSET  else C where C is a constant number that is small relative to the nominal value of I M . If C is made sufficiently small, the system will be stable for all expected values of current transfer ratio. C should be made sufficiently large so that the system settles rapidly enough to allow for setting I REF  and therefore optical output signal  115  in a acceptable period of time.       

   The performance of system  100  in  FIG. 2  can be quantified as follows. The response of the lightwave emitter to the bias current I B  may be represented as
 
P 115 =η*( I   B   −I   TH ),  I   B   &gt;I   TH   (9)
 
where P 115  is the average optical power coupled to transmission medium  170  and I TH  is threshold current of light emitter  110 . When I B  is less than or equal to ITH, P 115  is essentially zero. The average value of the modulation current, I M  in  FIG. 2 , may then be assumed to be zero, and does not change the average current in light emitter  110  or the average optical response.
 
   From equation 2, the average photodiode current is
 
I FB =γ*P 115   (10)
 
Equations 9 and 10 can be combined to yield
 
I FB =γ*η*(I B   −I   TH )  (11)
 
or
 
γ*η= I   FB /( I   B   −I   TH )  (12)
 
   According to equation 11, I FB  is linearly dependent on the quantity (I B −I TH ). Thus, the user may choose the value of I FB  when evaluating the left-hand side of the equation. Choosing the steady state value for the control system  100  in  FIG. 2  makes I FB =I REF . Thus, equation 12 can be written as
 
γ*η=I REF /( I   B −I TH )  (13)
 
In equation 13, I B  is the steady state bias current corresponding to I FB =I REF .
 
   The small signal gain of the lightwave emitter-lightwave detector pair using equation 11 is
 
 dI   FB   /dI   B   =d/dI   B [γ*η*( I   B   −I   TH )=γ*η  (14)
 
and using equation 13 is
 
 dI   FB   /dI   B   =I   REF /( I   B   −I   TH )  (15)
 
   The optical power emitted by the lightwave emitter in general is
 
 P=η* ( I   D   −I   TH )  (16)
 
where I D  is the total, as opposed to the average, current delivered to the lightwave emitter. The optical power emitted during the transmission of a logic high signal is
 
P 1 =η*(I 1   −I   TH )  (17)
 
and for a logic 0 or logic low signal
 
 P   0 =η*( I   0   −I   TH )  (18)
 
Where I D =I 1  and I D =I 0  are the values of total current delivered to lightwave emitter  110  for a logic 1 and a logic 0, respectively.
 
   The extinction ratio is the ratio of the optical power transmitted for a logic 1 to that for a logic 0, or
 
 E   R   =P   1   /P   0 =η*( I   1   −I   TH )/η*( I   0   −I   TH )=( I   1   −I   TH )/( I   0   −I   TH )  (19)
 
From  FIG. 10 , it may be seen that
 
I M =I 1 −I 0   (20)
 
   Thus, from equations 19 and 20 we can calculate
 
 E   R − 1 =( I   1   −I   TH )/( I   0   −I   TH )− 1 =( I   1   −I   0 )/( I   0   −I   TH )= I   M /( I   0−I   TH )  (21)
 
   It may also be seen from  FIG. 10  that
 
 I   B   =I   0   +r*I   M   (22)
 
where r is the duty cycle of the digital signal being transmitted. Subtracting I TH  from both sides of equation 22 gives
 
I B −I TH =(I 0 −I TH )+r*I M   (23)
 
   Combining equations 21 and 23
 
 I   B   −I   TH   =I   M /( E   R −1)+ r*I   M =I M *[1/( E   R −1)+ r]   (24)
 
   Substituting equation 23 into equation 15
 
 dI   FB   /dI   B   =I   REF   /I   M *[1/( E   R −1)+ r]   −1   (25)
 
   Let G(s) in equation 1 be written as
 
 G ( s )= A   O /( s*τ )* I   M   /I   REF   (26)
 
then from equations 1, 24, and 25 the loop gain is
 
 A=G ( s )*dI FB   /dI   FB   =[A   O /( s*τ )* I   M   /I   REF   ]*[I   REF   /I   M *(1/( E   R − 1 )+ r )] −1 =A O /( S*τ )*[1/( E   R − 1 )+ r]   −1   (27)
 
Let
 
τ O=τ/A   O *[1/( E   R −1)+ r]   −1   (28)
 
and
 
 A= 1/( s*τ   O )  (29)
 
τ O  is completely independent of the highly variable parameters η and γ. Furthermore, since ER and r are constants determined by the communications protocol, the effective time constant τo is constant and can be chosen as a design parameter. These characteristics arise directly from equation 26 as a consequence of making the gain of variable gain amplifier proportional to the modulation current and inversely proportional to the reference current. Equation 26 may be further simplified by choosing
 
 A   O=1 /( s*τ   O )  (30)
 
   With equation 30 equation 28 simplifies to
 
τ O =τ  (31)
 
and the time constant of the system is both constant and equal to the time constant of variable gain amplifier  150 .
 
     FIG. 5  shows one possible alternative embodiment  200  of the system shown in  FIG. 2 . In  FIG. 5  block  210  receives an input from I FB  instead of I REF . Block  210  divides I C  by I FB  to normalize the overall loop gain to a substantially constant value. In steady state, when I FB =I REF , the loop dynamics, such as loop bandwidth, are approximately the same as system  100  once steady state is reached. System  200  settles faster than system  100  because the loop gain is boosted during settling when I FB  is smaller than IREF. Block  210  is preferably configured to place a minimum limit on I FB  SO that it does not divide by zero and apply an infinitely large signal to multiplier  220 . 
     FIG. 6  depicts another alternative embodiment (system  300 ) of the system shown in  FIG. 2  in which signal processing block  310  determines the logarithm of the feedback signal I FB  before applying it to summing node  130 . Thus, block  310  produces a signal
   V   FB   =V   O *1 n ( I   FB   /I   o )  (32) 
   Where Vo and Io are constants. The incremental gain of block  310  is
 
 dV   FB   /dI   FB   =V   O   /I   FB   (33)
 
If the gain of variable gain circuit  190  is given by
 
 G ( s )=A o   /sτ*I   M   (34)
 
Then the loop gain is 
                   A   =       G   ⁡     (   s   )       *       dV   FB     /     dI   FB       *       dI   FB     /     dI   B                     =           A   o     /     V   o       /   s     ⁢           ⁢   τ   *     I   M     *       V   o     /     I   FB       *       dI   FB     /     dI   B                     =         A   o     /   s     ⁢           ⁢   τ   *       I   M     /     I   FB       *       dI   FB     /     dI   B                       (   35   )             
 
   According to equation 11, I FB  is linearly dependent on the quantity (I B −I TH ). Thus, the value of I FB  may be chosen when evaluating the left-hand side of the equation. Choosing the steady state value for the control system  300  in  FIG. 6 , we have I FB =I REF  and equation 12 may be written as
 
 A=A   O   /sτ*I   M   /I   REF   *dI   FB   /dI   B   (36)
 
   Substituting equation 25 into equation 35 gives 
                   A   =         A   o     /   s     ⁢           ⁢   τ   *       I   M     /     I   REF       *       I   REF     /     I   M       *       [       1   /     (       E   R     -   1     )       +   r     ]       -   1                     =         A   o     /   s     ⁢           ⁢   τ   *       [       1   /     (       E   R     -   1     )       +   r     ]       -   1                       (   37   )             
 
   Equation 37 shows again that the loop gain is independent of γ and η, and is therefore independent of the transfer ratio. One advantage of the alternative embodiment in  FIG. 6  is that the variable gain amplifier  190  need only perform multiplication by I M  rather than multiplication by I M  and division by I REF  (or I FB ). Both analog division and digital division are generally more difficult to perform than multiplication. Therefore, it may be preferable to take the logarithm of the feedback signal rather than dividing the control signal by the reference or feedback signal. Taking the logarithm of the feedback signal I FB  may also be preferred when I FB  has a very wide range of values, because the logarithm function has the well known property of compressing the range of its input signal. 
   System  500  in  FIG. 7  shows another alternative embodiment of the invention. In this case an adjustable resistor  187  with value R FB  converts the feedback signal I FB  to a voltage V FB :
 
 V   FB   =I   FB   *R   FB   (38)
 
   Resistor  187  is adjusted when system  500  is configured to obtain the desired optical power output P 115 . V REF  is a constant voltage. 
   The small signal gain of resistor  187  is
 
 dV   FB   /dI   FB   =R   FB   (39)
 
   Rearranging equation 38 and combining with equation 39
 
 dV   FB   /dI   FB   =V   FB   /I   FB   (40)
 
   In steady state, V FB =Vo, so equation 40 can be expressed as
 
 dV   FB   /dI   FB   =V   O   /I   FB   (41)
 
   Equation 41 is the same as equation 33. Let the gain of variable gain circuit  185  be given by equation 34. Then we can write the loop gain as 
                   A   =       G   ⁡     (   s   )       *       dV   FB     /     dI   FB       *       dI   FB     /     dI   B                     =           A   o     /     V   o       /   s     ⁢           ⁢   τ   *     I   M     *       V   o     /     I   FB       *       dI   FB     /     dI   B                     =         A   o     /   s     ⁢           ⁢   τ   *       I   M     /     I   FB       *       dI   FB     /     dI   B                       (   42   )             
 
   In deriving equation 13 it was shown that I FB  was equivalent to I REF , the value of I FB  in steady state. Thus, I REF  may be substituted for I FEB  in equation 25 and rewrite equation 42 as 
                   A   =       G   ⁡     (   s   )       *       dV   FB     /     dI   FB       *       dI   FB     /     dI   B                     =           A   o     /     V   o       /   s     ⁢           ⁢   τ   *     I   M     *       V   o     /     I   FB       *       I   FB     /     I   M       *       [       1   /     (       E   R     -   1     )       +   r     ]       -   1                     =         A   o     /   s     ⁢           ⁢   τ   *       [       1   /     (       E   R     -   1     )       +   r     ]       -   1                       (   42   )             
 
   This is precisely the same result obtained in equations 27 and 37. The loop gain is constant and independent of the highly variable quantities γ and η. 
     FIG. 8  shows one possible analog circuit implementation  350  of the system shown in  FIG. 6 . In  FIG. 8 , light emitter  110  may be a light emitting diode or laser diode. Light detector  120  is a photodiode that generates a current in proportion to the optical output of emitter  110 . Diodes  311  and  312  form circuit  310  and generate the logarithm of the detector output. Diodes  321  and  322  in circuit  320  generate the logarithm of the reference current signal  140 . Transistors  146  and  147  implement the functions of both summing circuit  130  and multiplying circuit  220  in  FIG. 6 . Transistors  148  and  149  form a current mirror that determines the difference of the collector currents in transistors  146  and  147  before applying the resulting current to integration capacitor  157 . 
   Darlington connected transistors  151  and  152  buffer the voltage on capacitor  157  and drive voltage-to-current converter  230  (formed by transistor  153  and resistor  154 ), which supplies bias current I B  to the light emitter  110 . Voltage-to-current converter  230  is preferably substantially linear so that its small signal gain is substantially independent of the magnitude of its current output. Current source  240  ensures startup of the bias current in the event that the modulation current and therefore the current in transistor  158  is zero. Current source  240  supplies a substantially constant current that is small compared to the nominal value of current I T . 
   Block  160  generates the modulation signal in response to a modulated input signal applied to the input node (i.e., the base of transistor  169 ) of current switch  164 . Voltage source  168  provides an appropriate reference so that current switch  164  alternately switches substantially none or substantially all of current I MT  into the collector of transistor  165 . Inductor  166  and capacitor  167  are preferably large enough that substantially all of the collector current of transistor  169  is routed to modulation signal I M  and therefore to light emitter  110 . The high output impedance seen at the collector of transistor  153  ensures that an insignificant portion of modulation signal I M  is absorbed. Current source  161  sets the modulation current level I MT  as well as current IT via the current mirror formed by transistors  162 ,  163 , and  158 . Transistors  162 ,  163 , and  158  preferably have predetermined relative emitter areas and therefore transistors  163  and  158  generate collector outputs that are in a predetermined ratio to current produced by current source  161 . 
     FIG. 9  shows one possible digital implementation  400  of the system shown in  FIG. 5 . Modulator  160  amplifies a communications signal, generating modulation signal I M  in proportion to amplitude control signal I MS . I MS , an analog signal, is generated from digital amplitude control signal  441  (I MSET ) by digital to analog converter  452 . Modulation signal I D  is applied to light emitter  110 , which is a light emitting or laser diode. Light detector  120  generates a current I FB  in response to optical signal  116  received from the light emitter. 
   Logarithmic amplifier  410  generates a signal proportional to the logarithm of I FB  and applies it to the input of analog to digital converter  450 . Digital summing circuit  430  determines the difference of digital reference signal  440  and the digital output of  450  to produce digital control signal I C . Digital multiplier  420  multiplies I C  by amplitude control signal I CS , which is proportional to digital amplitude control signal I MSET . Startup aid  445 , which can be implemented in a variety of ways, ensures that signal I CS  and therefore the gain of multiplier  420  is above zero, even when I MSET  is zero. The output of multiplier  420  is accumulated by digital accumulator  455 , which drives Digital to analog converter  451  and amplifier  230  to generate bias current I B . Bias current I B  drives the light emitter, closing the feedback loop. 
   Persons skilled in the art will recognize that the apparatus and methods of the present invention may be implemented using circuit configurations other than those shown and discussed above. All such modifications are within the scope of the present invention, which is limited only by the claims that follow.