Andrew, ZL2PD, contacted me regarding the matching scheme in a 25W 144MHz amplifier published in (ARRL 1977). The design no doubt appeared in many editions of the handbook. He was resurrecting an old build that just didn’t work as expected, and trying to understand why… which starts with understanding how it works, or should work.
Above is the schematic of the amplifier, analysis here is of the 25W configuration using a 2n5591.
The figure above shows the details of T1, a Ruthroff 1:4 unun.
The initial question was whether this would work as an air cored structure… but the question seemed motivated by difficulty in getting the amplifier to work properly.
Output matching review
So, let’s review the matching scheme. It is a combination of three components, T1, C4 and C5.
Consulting the datasheet, we see that the recommended load for the 2n5991 for 25W out on 12.5V at 175MHz is 4+j2Ω. That will be a little different at 144MHz due to the transistor capacitance having different susceptance at the lower frequency, but not greatly, it is a good place to start.
As mentioned there are three components in the matching network, but the operation of T1 is far from nominal 1:4, and for a transformation from 4Ω to 16Ω, you would choose a line with Zo=8Ω, that is not practicable, so there will be standing waves on that line section and therefore significant impedance transformation.
Transmission line characteristics
Since there is significant impedance transformation on the line, the characteristics of the line become important.
The originally specified #20 (0.81mm) was not on hand but some 0.71mm is available and will be used.
Minimum enamel thickness specified for 0.7mm wire ranges 30-80µm, let’s assume the medium covering of 53µm. Average cover may be a little more. The wire measures 0.755mm overall, but that alone does not imply the enamel thickness.
Using TWLLC, we can get a ball part estimate of Zo using a guess of vf=0.7 based on experience.
0.071 ECW twisted pair |
|
| Parameters | |
| Conductivity | 5.800e+7 S/m |
| Rel permeability | 1.000 |
| Diameter | 0.000710 m |
| Spacing | 0.000763 m |
| Velocity factor | 0.700 |
| Loss tangent | 0.000e+0 |
| Frequency | 146.000 MHz |
| Twist rate | 100 t/m |
| Length | 1.000 m |
| Results | |
| Zo | 33.50-j0.68 Ω |
| Velocity Factor | 0.7000 |
| Twist factor | 0.9725 |
So, Zo in the range 30-35Ω is likely.
A test section of 255m length was made and measured with SC and OC terminations using a VNWA3E.
Above are the |s11| measurements for SC and OC.
From that dataset we can calculate Zo.
Calculation of Zo over most of this range looks ok, it has the typical turn up at low frequencies, and there is a problem measuring close to its quarter wave resonance. Around 150MHz, Zo is around 33Ω, quite close to expectation.
We can also calculate vf.
vf is 0.665 around 150MHz, so the earlier guess was not too far off the mark.
Simsmith model
Let’s build a Simsmith model to find a matching solution and explore the sensitivity to component values.
Taking the target load impedance for the source to be 4+j2Ω, we can use Simsmith to model the network and tweak it for a match to a 4+j2Ω generator.
Element D models the Ruthroff 1:4 unun transmission line transformer. Lcm is a calculated value for the common mode inductance of the transmission line section, a two turn solenoid to accommodate the length of the transmission line section.
It is not very convenient to work with a Smith chart with complex reference impedance, as can be seen it warps the Z space.
Instead, let’s add an element so that we can use a purely real Zo.
Above, Z1 offsets the j2 component of the desired network input impedance so that the Zo is 4Ω for a ‘normal’ Smith chart scaling. Z1 is not part of the actual network, but purely a fixup.
Element D models the Ruthroff 1:4 unun transmission line transformer. Lcm is a calculated value for the common mode inductance of the transmission line section, a two turn solenoid to accommodate the length of the transmission line section.
If you follow the impedance changes at each element of the Simsmith model, C2 and D are the most significant (excluding from the dummy Z1). Impedance transformation in D is mostly due to transmission line effects.
Not surprisingly, matching is very sensitive to C2 and length, vf and Zo of the transformer D. As it turns out, the common mode inductance Lcm is not very critical, hence no need for a magnetic core.
Conclusions
- Analysis of the Simsmith model would suggest that this design is highly sensitive to the twisted pair transmission line wire diameter, enamel covering and length and would appear to not be easily reproduced.
- There is a certain amount of adjustment by trial and measurement for designs at this frequency, but this design appears to require more than better designs.
References
ARRL. 1977. The radio amateurs handbook. ARRL p453