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Guy's,
Although Vcc/2 bias resistors (R5/R3) were added -- its center point cannot go to the minus input of the DAC. If the (-) side of the DAC is ground, then this will hold the bias point essentially at ground and obviate the purpose of the divider. Also, this bias point is going to try and backdrive the DAC (-). The "Vsl-" point should be disconnected from the bias resistors and connected to ground.
However, much more importantly, the LM741 output will never be less than +0.7V (as Sarge noted, it will be inside the rails). As a matter of fact, the output will probably only go as low as +1.5V at best. This means that the xstr Q1 will ALWAYS be turned on to saturation (>0.7V), and will never be off or have a chance to function in the linear region. The regulator will forever output approx. 1.25V.
Having an input up to +5V from the DAC, the op amp will uselessly try to drive Q1 harder and only eat more power. Also consider that without a series base resistor the op amp is essentially driving a diode drop to ground, which is why it's over-heating (but, this is a rather moot point in light of the above issue).
Sorry man, but Sarge's circuit is plagued with design issues.
You could eliminate Q1 and drive the regulator directly (similar to my suggested circuit), but the minimum voltage would be the minimum output of the op amp plus +1.25V (or, approx. +2.75V), which does not meet your minimum output voltage criteria of +1.25V (you'll need a negative supply to get this). The max output (with a gain as shown of Av = 1), would be 5V + 1.25V = +6.25V which does not meet your maximum output voltage criteria of +8V. So, you would need to modify your minimum output criteria as noted, and change the design for a minimum gain of Av =1.6. Also, the op amp required must have the capacity to drive 10mA at the required +6.25V output voltage.
P.S.
In my above quote "...I am not showing any bypass caps that may be required."
Note I didn't say they weren't needed (*required*), I simply omitted them for schematic simplicity.
Although Vcc/2 bias resistors (R5/R3) were added -- its center point cannot go to the minus input of the DAC. If the (-) side of the DAC is ground, then this will hold the bias point essentially at ground and obviate the purpose of the divider. Also, this bias point is going to try and backdrive the DAC (-). The "Vsl-" point should be disconnected from the bias resistors and connected to ground.
However, much more importantly, the LM741 output will never be less than +0.7V (as Sarge noted, it will be inside the rails). As a matter of fact, the output will probably only go as low as +1.5V at best. This means that the xstr Q1 will ALWAYS be turned on to saturation (>0.7V), and will never be off or have a chance to function in the linear region. The regulator will forever output approx. 1.25V.
Having an input up to +5V from the DAC, the op amp will uselessly try to drive Q1 harder and only eat more power. Also consider that without a series base resistor the op amp is essentially driving a diode drop to ground, which is why it's over-heating (but, this is a rather moot point in light of the above issue).
Sorry man, but Sarge's circuit is plagued with design issues.
You could eliminate Q1 and drive the regulator directly (similar to my suggested circuit), but the minimum voltage would be the minimum output of the op amp plus +1.25V (or, approx. +2.75V), which does not meet your minimum output voltage criteria of +1.25V (you'll need a negative supply to get this). The max output (with a gain as shown of Av = 1), would be 5V + 1.25V = +6.25V which does not meet your maximum output voltage criteria of +8V. So, you would need to modify your minimum output criteria as noted, and change the design for a minimum gain of Av =1.6. Also, the op amp required must have the capacity to drive 10mA at the required +6.25V output voltage.
P.S.
In my above quote "...I am not showing any bypass caps that may be required."
Note I didn't say they weren't needed (*required*), I simply omitted them for schematic simplicity.
