By Anna N. Rudiakova, Vladimir Krizhanovski
Complex layout concepts for RF strength Amplifiers presents a deep research of theoretical points, modelling, and layout innovations of RF high-efficiency strength amplifiers. The booklet can be utilized as a advisor via scientists and engineers facing the topic and as a textual content publication for graduate and postgraduate scholars. even if basically meant for knowledgeable readers, it offers a superb quickly begin for newbies.
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Then, the set of two algebraic equations can be obtained as follows: SVBE °°− 3ω0τ S a3 + b3 = 6π B3 , ® °3ω τ b + a = SVBE A 3 3 °¯ 0 S 3 3π (2-17) where ( ) A3 = sin θ1 cos 2 θ1 (3 cosθ1 − 4 cosθ ) + cosθ sin 3 θ + sin θ1 , B3 = 3cos2 θ1 − 6 cos 4 θ1 + 3cos 2θ −2 cos 4 θ + 2 cos θ cos θ1 ( 4 cos 2θ 1 − 3) . Therefore, the third harmonic Fourier coefficients can be found as follows: Theoretical Analysis of BJT Class-F Power Amplifier a3 = SVBE 2 A3 − 3ω0τ S B3 , ⋅ 6π (3ω0τ S ) 2 + 1 b3 = SVBE 6ω0τ S A3 + B3 , ⋅ 6π (3ω0τ S ) 2 + 1 I3 = SVBE 6π 41 4 A3 + B3 , (3ω0τ S )2 + 1 2 2 § 6ω0τ S A3 + B3 · ¸¸ .
2-6) and (2-8), the dependence of I C (v j ) should be approximated as follow24: I C = S j (v j − E ' ) v j >E ' (2-9) where S j = β DC / rβ is the transconductance of the collector current on the base-to-emitter junction. The piecewise linear dependencies of I B (VBE ) , and I C (V BE ) for the low frequencies can be obtained by substitution of Eq. (2-8) into (2-5) as follows24: I B = S b (VBE − E ' ) V I C = S (V BE − E ' ) V BE > E ' BE > E ' where S b = 1 /(r 'b + rβ ) ; S = β DC S b = [rβ /(r 'b + rβ )]S j .
The expressions for the network elements’ impedances are the following: Q 2 > R1 R2 − 1 , R1 R2 > 1 , (1-39) X L = QR2 , (1-40) X 1 = R1 X2 = ( ) R2 1 + Q2 −1 , R1 § R1 ¨Q + R1 R2 − 1 ¨© ( ) · R2 1 + Q 2 − 1 ¸¸ , R1 ¹ X1 R1 (1-41) XL X2 R2 Figure 1-21. Example of input matching network. (1-42) Introduction to the RF Power Amplifiers Design 27 where q is the quality factor, and should be given. The certain inductance or capacitance should be calculated for the given frequency f 0 as L = X /( 2π f 0 ) , C = 1 /(2π f 0 X ) , respectively.