RF Amplifier

This is the story of a design for a class-E amplifier used to drive a photoconductance decay rig.  RF power is coupled into a silicon wafer and used to measure carrier statistics.  To make this a stable piece of laboratory equipment, the design started with a power analysis by adding up the desired signal level and all the power drops in the system. For good signal to noise ratio, a measured signal level of 500mV was chosen. This is equivalent to +7dBm.  Details of the rest of the testing setup are in another post but the power losses meant a minimum of +31dBm source power for +7dBm received power. Radio frequency design involves quite a bit of tweaking beyond initial specs so a source power of +36dBm (or almost double +31dBm) was chosen. From this value, all the components for the amplifier were chosen.

A unique property of this source is the requirement to operate at only one frequency. The source will never be modulated and merely has to produce a single frequency sine wave. Due to this limiting condition, some efficiency enhancing techniques can be used. At +36dBm, the source power is 4W and will be driven through a single output transistor. In order to keep power dissipation down, a resonant class-C amplifier architecture was chosen.

The class of an amplifier is tied to the operating period of the transistor during a sine wave. Class-A amplifiers bias the transistor on for the full cycle and are the least efficient. Class-C resonant amplifiers turn the transistor on for a small fraction of the sine wave cycle. By utilizing resonant elements, harmonic content is filtered out to leave the desired frequency. This circuit is operated in Class-C mixed mode where the output capacitance of the driving transistor is used as a resonant element instead of ignored. Efficiency in a class-C amplifier can exceed 75% and is a great improvement over the maximum of 25% in a class-A.

Resonant vs linear amplifier classes

Resonant vs linear amplifier classes

Working backwards from the 4W output requirement, the individual transistors can be chosen. The NTE341 NPN transistor was chosen as the output transistor due to its 4W output power and 12dB gain. The input power requirement still needs an additional 24dB of gain so another amplification stage is required. The NTE346 NPN transistor was chosen as the gain stage for its 1W output power and 10dB gain. The gain requirement is now down to 14dBm which was easily accomplished with a Gali-24 monolithic amplifier from MiniCircuits. With the maximum output of a source at 0dBm, each stage has sufficient gain to create the desired output power.

Power levels in RF amplifier chain

Power levels in RF amplifier chain

A common question in RF design is how an amplifier operating at 12V can output 4W into a standard 50ohm load. It seems that the maximum power would be just over 2W instead. To obtain 4W output, the load has to be transformed using a matching network. This is where class-C architecture benefits by having the ability to integrate impedance transformations into the output stage. As with the power calculations, the total design starts at the output stage and moves toward the input. For a 12V supply to produce 4W output, the effective load the output transistor needs to “see‟ is 12.5ohms.

    \[R_L=\frac{\left( V_{CC} - V_{CE(sat)} \right)^2}{2P_{out}}\]

 

Output driver transistor load matching

Output driver transistor load matching

To obtain this match, a Pi transformation network was designed to present 12.5ohms to the transistor and 50ohms to the load at 100MHz.

Pi-transform network on output transistor

Pi-transform network on output transistor

The values for the output Pi network are calculated to match at the operating frequency of 100MHz with a bandwidth of +/- 10MHz. This gives a quality factor, Q, of 100/20 or 5. By choosing the bandwidth, the matching network was designed to approximate the specified impedance values over the frequency range chosen as described in Krauss.

    \[X C_1 = \frac{R_L}{Q} \to 2.5 \]

    \[X C_2 = R_0 \sqrt{\left(\frac{\frac{R_L}{R_0}}{(Q^2+1)-\frac{R_L}{R_0}}  \right)} \to 4.93 \]

    \[X L=\frac{Q R_L + \left(\frac{R_L R_0}{X C_2} \right)}{Q^2+1} \to 7.28\]

At the operating frequency of 100MHz, the values become: C1=637pF, C2=323pF, and L=11.5nH. The output impedance of the transistor itself is usually only given by a single output capacitance, C0. This capacitance can then be included in the value for C1 to get a corrected value. For the NTE341, the output capacitance is 180pF for a corrected value of C1=457pF. The nearest standard value for C1 is 470pF and the nearest standard value for C2 is 330pF. A small air-core inductor is used for L and its dimensions are given by the Wheeler formula where D is the diameter in inches, H the height in inches, and n the number of turns.

    \[L = \frac{n^2 D^2}{18D + 40H} \]

An inductor of 22ga magnet wire wound around a 1/8” former with 5 turns and a height of ½” was used.

Output transistor matching network with values

Output transistor matching network with values

 

With a basic output network, the task of properly biasing the transistor was approached. A ferrite bead was connected from the base to ground providing a DC reference and an inductor connected between the collector and Vcc. When the transistor is on, current is directed to ground and energy begins to build in the choke. As the transistor turns off, the energy stored in the choke is delivered to the output matching network where the harmonics are removed. As opposed to a resistor bias, inductively coupling the collector allows the output voltage to swing a full +/- Vcc.

The actual sizing of the collector inductor should be considered as a means for improving efficiency further. If the choke is very large, the collector voltage will not fall before the next cycle begins. When the transistor turns on, the high collector voltage has to be shunted to ground creating a current pulse that dissipates as heat in the transistor. If the choke is too small, the collector voltage will drop to zero before the transistor turns on again and the output will not be sinusoidal. Most RF circuits describe this as a choke having very large inductance. Here, it is changed to Lbias to reflect the efficiency gains possible by properly sizing this component. A good starting point for the inductance is the output collector impedance divided by four times the frequency.

    \[L_{bias} \sim \frac{R_L}{4f} \to 31nH \]

Collector voltage with varying inductor values

Collector voltage with varying inductor values

Each stage of the amplifier has to be impedance matched to the stage following it. The design for impedance matching has to include some tuning elements because the datasheets for RF transistors do not have accurate specifications for the input and output impedance. This is as simple as using variable capacitors and air-core inductors. With the output and bias networks calculated, the input matching network for the output transistor stage can be calculated.

For a +36dBm output from the final stage, the prior stage has to produce +24dBm or 250mW. Using the equation for load impedance, the effective load impedance is calculated to be 200ohms. It is again necessary to transform the output impedance of the gain stage to match the input impedance of the output stage.
Calculating the impedance match between the gain stage and the output stage starts with the same technique of calculating the required power first.

 

Input matching for output driver transistor

Input matching for output driver transistor

Since the impedances being transformed are very different, the selectivity of the filter will be very narrow. This is addressed in the second iteration of the design by transforming through an intermediate impedance in two stages. To properly transform the impedances, a Q of 10 is chosen. The expected impedance from the left is denoted R1 and the real part of the input impedance on the right is denoted R2.

    \[X C_3 = R_1 \sqrt{\left(\frac{R_2}{R_1} \right) (1+Q^2)-1} \to 143.5 \]

    \[X C_4 = \frac{R_2(1+Q^2)}{Q-\sqrt{\left(\frac{R_2}{R_1} \right)}(1+Q^2)-1} \to 32.6 \]

    \[X L = Q R_2 \to 30 \]

The reactive part of the 3-j3.8 input impedance is in series with the inductor and can be combined with it for an equivalent XL=26.2. At 100MHz, these values become: L=42nH, C3=11pF, and C4=48pF. In practice, the inductor is a ¼” diameter, 3/8” long coil with 5 turns. The 11pF capacitor was replaced with a 10pF trimmer and C4 is the nearest standard value of 47pF. The final circuit for the output driver stage having both the input and output matching networks is shown here.

Output transistor driver circuit with all matching and bias components

Output transistor driver circuit with all matching and bias components

The primary amplification stage utilizing the NTE346 transistor boosts the signal from +14dBm to +24dBm and follows a similar design procedure to the output stage. However, since it is a much lower power, the transistor is operated in class-A instead of class-C. This eliminates the need for harmonic filtering between the stages and maintains low distortion. Choosing class-A operation sacrifices efficiency at the sake of simplicity. Biasing the base for a common emitter class-A amplifier is easily accomplished with resistors. The collector is connected to Vcc through an inductor similar to the output stage to allow the full voltage swing of +/-Vcc.

Inductively-coupled Class-A gain stage circuit

Inductively-coupled Class-A gain stage circuit

The resistors RB1 and RB2 form a resistor divider network to set the DC base voltage of the transistor. For an output of 250mW into 200ohms, the collector current will be 50mA. The DC current gain of the NTE346 is 100 indicating that the base current needs to be 500uA or larger. The bias resistors are chosen to ensure this condition with RB1=33k and RB2=10k. The collector inductor is calculated as before for an LC=500nH. In practice, this value was decreased to LC=100nH because it provided the best performance. These calculations at radio frequencies represent a good starting point and the real values can only be obtained with tuning. With the bias networks calculated, all the components for the 2nd and 3rd stage of the amplifier can be combined. The first stage is simply a monolithic amplifier capacitively coupled into the 2nd stage.

Full gain-stage and output-driver circuit

Full gain-stage and output-driver circuit

NOTES:  Following the first iteration of this circuit, a number of simplifications and improvements were made. The RF generator was integrated on board with a MiniCircuits JTOS-150 voltage controlled oscillator. The drive frequency could then be easily adjusted from a potentiometer integrated into the circuit. Power levels were adjusted with a MiniCircuits MVA-2000 voltage-variable attenuator. All signal generation and level adjustment could be done on board from the same unit.