Pi-L & Pi Output Networks for RF Power AmplifiersAuthor: R.J.Edwards G4FGQ © 13th January 2001
APi-L or Pi network's primary function is to transform an external load resistance to a value commensurate with an amplifying device's voltage and power ratings.
There are two parts to the associated program. For a given RF power output, peak anode (plate) voltage, and external load resistance, the first part computes theoretical L & C component values, efficiency, etc. The second part allows network component values to be varied in small increments over wide ranges from the keyboard. Tuning capacitor C1 and loading capacitor C2 can be varied as in an actual transmitter while observing the resulting changes in load impedance presented to the power amplifying device: triode vacuum-tube, tetrode vacuum-tube, bipolar transistor, field-effect transistor (FET), etc.
The network also functions as low-pass filters to filter-out harmonics of the carrier-frequency generated in the amplifying device when running under class AB linear or class C high-efficiency operating conditions. The reason for using a Pi-L network rather than the simpler Pi network or merely a simple tuned-tank circuit is the Pi-L network's greater harmonic rejection.
The harmonic rejection computed by the program is relative to the carrier frequency voltage-level at the network's input. The actual harmonic output level depends additionally on the ratio of harmonic-to-carrier voltage ratio developed by the amplifier itself. It is assumed the network is terminated at harmonic frequencies by the same value of load resistance as at the fundamental frequency. In practice an antenna feed-line input impedance at harmonics is indeterminate and computed rejection levels are therefore only approximations.
After entering the amplifier's power and voltage ratings a circuit designer still has two degrees of freedom to make use of. He can choose the phase-delay angles of both the Pi and L sections. In some applications it is necessary to control phase delay, but usually this parameter is of no consequence. Entering two angles into the model allows the designer to indirectly exercise control over harmonic rejection or obtain more convenient or practical values of L and C. If the L-section phase-delay is set to zero degrees the circuit reduces to a simple Pi-network. If set to high angles, harmonic rejection may be theoretically good, but the coils may have an impractical inductance values and low Q.
135 degrees of phase shift in a Pi section is an interesting value. As may be demonstrated by means of the program, around this angle it is found that interaction between the tuning and loading controls is minimized. Capacitor C2 can be varied to adjust the anode (plate) load resistance over a range of values with negligible effect on the load-angle and the amplifier will remain in tune without the need to alternate back and forth between settings of C1 and C2.
The range of available load resistances before retuning becomes necessary can be increased still further by mechanically linking the tuning of L2 to C2.
It is desirable to maintain a relatively low harmonic-voltage at the output of the amplifying device, i.e., the RF voltage change should be a nearly-perfect sinusoidal waveform. The operating Q of the equivalent tank-circuit ideally should not be less than 7 or 8, and to avoid excessive loss in L1, its Q is not normally made greater than about 12.
Theoretical network values of L and C do not in practice provide the exact value of ideal load resistance for an amplifying device. This is mainly due to the intrinsic Q of coils. The Q of a coil for a 50-watt, 2 MHz power amplifier in a metal enclosure usually is in the range 150-250. For the same size coil, coil Q tends to increase with frequency. Q also increases with physical size, so a coil for a 1500-watt, 30 MHz power amplifier might have a Q in the range 500-800. Highest Q values are obtained when a metal screening enclosure is very much larger than an enclosed coil.
1) Losses in C1 and C2 are ignored in program calculations.
2) By setting the L-phase delay in the associated program equal to zero, so L2 = 0, Pi-L network calculations become calculations for a simple Pi-network.
Run this Program from the Web or Download and Run it from Your Computer
This program is self-contained and ready to use. It does not require installation. Click this link Pi_L_Net then click Open to run from the web or Save to save the program to your hard drive. If you save it to your hard drive, double-click the file name from Windows Explorer (Right-click Start then left-click Explore to start Windows Explorer) and it will run.
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