WE2D-1

Split-Band Modulator for Kahn-Technique Transmitters Frederick H. Raab

Green Mountain Radio Research Company, Colchester, VT, USA

A b m a d - Kahn-technique transmitters exhibit high etliciency over a wide dynamic range of amplitudes and therefore also exhibit high average efficiencies for amplitude modulated signals. Their bandwidth is, however, limited by that of their class-S modulator. The split-band modulator described here combines a class-S modulator and a elass-B linear amplifier to provide greatly inereased bandwidth [from 25 kHz to 5 MHz) at the cost of a small reduction (10 percent) in efficiency. A NegativeCompouent Signal Processor provides driving signals that allow hotb amplifiers to operate efficiently into resistive loads. Linear class8 ampliriers can be implemented with bandwidths of 100 MAL The split-band modulator thus makes possible the use of the Kahn technique in wideband applications such as W-CDMA, base stations, and satellite repeaters.

Index Terms - Power amplifier, transmitter, modulator, amplifier.

I. KAHN EER TECHNIQUE

The Kahn Envelope-Elimination-and-Restoration (EER) technique produces amplitude-modulated signals with high efficiency by combining a saturated RF power amplifier (PA) and an efficient high-level amplitude modulator (Fig. 1). Operation of the RF PA in saturation ensures that it achieves the maximum possible efficiency. The high-level amplitude modulator varies the supply voltage of the RF PA to control the amplitude of the RF output. Phase information is conveyed to the output through the RF drive. Given an efficient modulator, high efficiency is maintained for all output amplitudes. Kahn- technique transmitters have been demonstrated from LF through L band [1],[2] and exhibit three to five times the

p DC SUPPLY

MODULATED WPPLY

Fig. 1. Kahn-technique transmitter.

average efficiency of linear amplifiers for signals with high peak-to-average ratios.

The bandwidth of a Kahn-technique transmitter is limited by that of its high-level modulator. Kahn- technique transmitters implemented to date use high- efficiency class4 modulators, which are a type of dcdc converter configured for linear amplification. The bandwidth of the envelope modulation must be at least twice that of the RF signal [3]. The switching 6equency of the class-S modulator must be 6 to 7 times the RF bandwidth to ensure adequate attenuation of the switching hquencies and sufficiently small spurious modulation products within the output hand [4].

Most modulators are designed to date switch at 250 to 500 ICHZ. This provides an RF bandwidth ofup to 50 IrHz, which is adequate for most legacy signals as well as NADC TDMA. Switching frequencies of 1 to 10 MHz should be possible, especially with IC implementations. However, it is doubtful that modulators for widehand applications (switching 6equencies of 30 to 100 MHz) are practical.

11. SPLIT-BAND MODULATOR

The bandwidth of a class-S modulator can he extended by combining it with a class-B linear PA (Fig. 2). The class4 modulator efficiently amplifies the lower- 6equencies that constitute most of the power in the envelope. The class-B PA adds the smaller amount of power in the higher-frequency components. A modulator of this type was first used in the Kahn transmitter in the amateur-radio satellite OSCAR 7 [5].

Previous split-band modulators use passive diplexers to split the drive signal. As a result, the load impedances presented to the two PAS vary erratically 6om well below to well above the transition 6equency, resulting in erratic power consumption, transfer of power 60m one PA to the other, and erratic gain in the transition region.

A flat 6equency response with linear phase is necessary for low IMD in the RF-output signal, and resistive loads are necessary for efficient operation of the two PAS in the modulator. These two objectives are achieved by the modulator shown in Fig. 2[6]. The output diplexer is a classic Butterworth design [7] with the z e r ~ R ends of the filters connected together at the load. The Negative-Component Signal Processor (NCSP) uses mirror-images of the output filters with negative

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07803-8331-1/04/$20,00 0 2004 IEEE 2004 IEEE M'IT-S Digest

NEGATIVE-COMPONENT SIGNAL PROCESSOR - - - - - - - CLASS-S ' -L

I = 2

Fig. 2. Split-hand modulator

components to provide the amplitudes and phases needed to drive the two amplifiers. The NCSP is implemented in DSP where the effects of negative components can be realized as easily as those of positive components. This produces resistive loads at all frequencies and a smooth transition of output power kom one amplifier to the oaer, flat system gain, and constant phase (Fig. 3).

0.1 1.0 10.0 SIB,

Fig. 3. Ideal frequency responses.

The power-division ratio a is the ratio of the envelope power that can be amplified by the class-S modulator (Bequencies up to Bs) to the total envelope power. The average efficiency depends upon the efficiencies of the class-S modulator and -B PA, as well as a, i.e.,

~ A V G = l / [ a q s + ( l - a ) q l g I . (1)

The principal characteristics of the envelope that affect modulator performance are the distribution of power over frequency and the peak-to-average ratio of the high- fkquency component of the envelope. The effects of bandwidth are most readily evaluated with multi-tone signals, while the effects of peak-to-average ratio 5 are most readily evaluated with noise.

111. MULTI-TONE SIGNALS

The variations of power-division ratio a with the bandwidth of the class-S modulator are shown in Fig. 4 for various multi-tone signals. For most waveforms, approximately 80 percent of the power is contained in the dc component, and 99 percent of the power occurs at frequencies less than the RF bandwidth Em.

The high-frequency portion (EH) of the envelope contains the peaks in the envelope, and its peak-to-average ratio E,H increases with the bandwidth of the class-S modulator, resulting in less efficient operation of the clas!;- B PA. The best efficiency is obtained by setting the supply voltages of the class-B PA to match the peaks in EH. The average efficiency of a complete modulator with ideal class-S and class-B PAS is shown in Fig. 5 . The average enlciency for ten 10-tone signals with randomized phases is 88 percent when the bandwidth of the class-S modulator is negligible and climbs to 99 percent when B s = E m .

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1.0

a

0.5 - W I M WISE

0.0 0 1 2

B s / B ~ ~ Fig. 4. Power division for multi-tone signals.

1.0

~ A V G

0.5

- 1 TONE - 10 TONE RIlocy

10 TWE CUiEWNT

0.0 0 1 2

B d B ~ ~ Fig. 5. Average efficiency vs. bandwidth.

N. NARROW-BAND GAUSSIAN NOISE

The composite of multiple independent carriers tends toward a random phasor sum. This is equivalent to narrow-band Gaussian noise and has a Rayleigh- distributed envelope [8]. The power spectrum of the envelope [9] consists of a dc component, a component that decreases linearly with frequency until f = B w , and a

component that varies as llfs for higher frequencies. For fc B m , the powerdivision ratio is therefore

a = d 4 + 0.415 [ (BS/BRF) - ( B ~ B w ) ~ / ~ ] . (2)

When the bandwidth of the class-S modulator is low in comparison to that of the RF signal, the performance of the split-band modulator can be analyzed by dividing the envelope into dc and ac components. For a peak-to- average ratio c,, the dc component is (d25)”2. The PDF

of the ac component EH is a Rayleigh PDF shifted so that its mean i s zero. The dynamic range of the class-B PA is that of the original envelope, but the negative and positive peaks are lower than the peak of the original envelope. For most efficient operation, supply voltages of the class- B PA are set to match the negative and positive peaks.

Because of tbe asymmeby in the PDF, the average power is reduced by more than the peak power, causing the peak-to-average ratio 6,y to be higher than tbat of the RF signal. For an RF signal with a typical 5 = 10 dB, = 13.8 dB. For higher peak-to-average ratios, the increase can be as high as 6.7 dB.

The variation of the average efficiency with the peak- to-average ratio of the RF signal is shown in Fig. 6 and summarized in Table 1, The average efficiency of an ideal split-band modulator is around 90 percent for low peak-to- average ratios, but drops steadily with increasing peak-to- average ratio. For 5 = 10 dB, the average efficiency drops to 73 percent, but is nonetheless more than double that of a linear class-B modulator. For 5 = 20 dB, average efficiency is improved by a factor of 3.5.

~ A V G

0.5

Fig. 6. Average efficiency vs. peak-to-average ratio.

Table 1. Average efficiencies of ideal modulators.

SIGNAL 5,dB a ~ A V G Lin/B SB/B SBIG

smc 3.8 0.954 0.660 0.9158 0.926 Noise 5.0 0.812 0.579 0.8643 0.888 Noise 10.0 0.786 0.357 0.7276 0.843 Noise 15.0 0.785 0.201 0.5457 0.778 Noise 20.0 0.785 0.113 0.3777 0.630

The efficiency can be further improved for signals with higher peak-to-average ratios by using a class-G amplifier [lo] instead of a class-B amplifier. The addition of a

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second positive supply voltage at approximately 3/8 of the main positive supply voltages keeps the average efficiency above 80 percent for peak-to-average ratios up to 14 dB.

V. EXPERIMENTAL RESULTS

A prototype split-band modulator is implemented by combining an existing class-S modulator with a power op- amp (Apex PA19). Single-tone signals with appropriated amplitudes and phases are generated by a multi-channel programmable-mvefonn generator. The class-S modulator switches at 250 &. The three-pole diplexer has a transition frequency of 25 ~Hz.

The variations of gain and efficiency with frequency are shown in Fig. 7. At lower fiequencies, the system efficiency is 72 to 75 percent. The efficiency is reduced h m the 90 percent of the class-S modulator by the quiescent current of the op-amp. Above the transition frequency, the efficiency drops to 62 to 65 percent as the op-amp takcs over amplification. The increase in efficiency at the highest fiequencies is due to increased inductance in the load, which results in lower output current.

The gain is k t within 0.8 dB through the transition region. The gain variation is thought to he due to deviations in the diplexer components from their design values. Overall, the 5 0 - H ~ bandwidth of the class-S modulator is extended to 5 M H z with a small reduction in efficiency.

REFERENCES

[I] F. H. Raab and D. J. Rupp, ”High-efficiency multimode HFNHF transmitter for communication and jamming,” Proc. MLCOMW, Ft. Monmouth, NJ, pp. 880 - 884, Oct. 2 - 5, 1994.

[2] F. H. Raab, B. E. Sigmon, R. G. Myers, and R M. Jackson, “L-band “&er using Kahn EER technique,” IEEE Trans. Microwave Theory Tech., pt. 2, vol. 46, no. 12, pp. 2220 - 2225, Dec. 1998.

[3] F. H. Raab, “Intermodulation distortion in Kahn technique transmitters,“ IEEE Trans. Microwave Theory Tech., vol. 44, no. 12, part I , pp. 2213 - 2278, Dec. 1996.

[4] H. L. Krauss, C. W. Bostian, and F. H. Raab, Solid State Radio Engineering. New York Wiley, 1980.

I. Hz

Fig. 7. Measured performance of prototype modulator.

[5] K. Meinzer, “A linear transponder for amateur radio satellites,” VHF Communications, vol. I, pp. 42 - 57, Jan. 1975.

[6] F. H. Raab, “Technique for wideband operation of power amplifiers,” U.S. Patent 6,252,461, June 26, 2001.

diplexer filters,” RFDesign, vol. 9, 00.11, pp. 92-99, Nov. 1986.

[8] F. H. Raab, “Average efficiency of power amplifiers,” Proc. R F Technology Expo ‘86, Anaheim, CA, pp. 474 - 486, Jan. 30 - Feb. 1,1986.

modulated components of mow-band Gaussian noise,” IRE Trans. Info. Theory, vol. IT-I, pp. 9 - 13, Sept. 1955.

amplifiers,” IEEE Trans. Consumer Electronics, vol. CE-32, no. 2, pp. 145 - 150, May 1986.

[7] F. Methot, “Constant impedance bandpass and

[9] R Price, “A note on the envelope and phase-

[IO]F.H. Raab, “Average efficiency of ClassG power

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