Watt meters which are built using an analog meter for the indicator require redoing the meter scale. This is because power is a squared function of the detected voltage. Therefore, one must calibrate the meter at quite a few points. Typically for a QRP watt meter we would mark the .5, 1, 2, 3, 4 and 5 watt points on the meter. Reading power which doesn't fall on one of the calibration "ticks" is often misread, as half way between say the 1 and 2 watt marks is not 1.5 watts. Its more like 1.25.
The way to solve this problem is to use an analog multiplier circuit to square the detected voltage from the SWR bridge. Looking though an old National Semiconductor Linear applications book, I found a reasonably simple circuit which will square an input voltage and convert it to a current suitable for driving an analog meter. I put one together and it works great.
This circuit does have a few quirks.
One, it requires the use of dual transistors. The application note shows the use of LM394 super matched pair transistors, in a TO-5 can. These are still available, but at over $5.00 each and you need two sets. I happened to have a couple CA3046 transistor arrays to use.These are still available from Jamesco. If you don't mind using SMT parts, Digi-Key has a MMPQ2222ACT in a 16 pin SOIC package, which is a 2N2222A transistor array.
I did try using 2N3904 transistors, but there is excessive drift due to temperature. Just putting a finger on one of the transistors causes radical meter drift. Its remotely possible one could get these to work by thermally bonding them to a common piece of aluminum.
The original circuit required a regulated negative supply. This required powering the circuit with two 9 volt batteries. I was able to modify the circuit so it would run on a single 9 volt battery. This was achieved by using a LM317L adjustable voltage regulator to create a "pseudo ground". The output of the regulator is connected to circuit ground, while the negative end of the battery is left floating. The regulator keeps a constant voltage between ground and the negative side of the battery. This allows the output of the op amp to swing negative in respect to ground, which is required to make the circuit work.
Q1 in the op amp feedback loop squares the current, because of the current gain relationship between the emitter and collector currents. Q4 mirrors the current in order to drive the meter. Replacing the meter with a resistor would give a voltage output, which could go to a DVM.
I used a CA3140 op amp, because I had them and its output will go to the negative rail. A CMOS rail to rail output op amp could be used instead and a LM358 should work as well.
V2 in the diode componsation circuit shown later is used to calibrate the meter. Increase the value of R1 to make the meter less sensitive, should you want to measure higher power levels. I happened to have a nice 500 uA meter with a 0-500 scale to use. Meters with other sensitivities could be used, adjust the value of R1 to compensate.
Here is a diode compensation circuit which linearizes the SWR bridge detector diode. This circuit "adds back" the forward drop of the detector diode and compensates for the non-linear response of the detector diode at low input voltages. This results in greatly improved accuracy. U1 needs to be a rail to rail output type so the output can go to ground. Two of these circuits are needed if accurate reverse power is to be measured.