A double-tuned amplifier has a load as shown in Fig. 4.24(a). The center frequency of the response is 2 GHz. Effective quality factors of both sides were adjusted to 20 with an appropriate Q-enhancement circuit, which corresponds to a parallel effective resistance of Rp1 = Rp2 = 2512 ohm.

Question

A double-tuned amplifier has a load as shown in Fig. 4.24(a).

The center frequency of the response is 2 GHz. Effective quality factors of both sides were adjusted to 20 with an appropriate Q-enhancement circuit, which corresponds to a parallel effective resistance of [latex]R_{p1} = R_{p2}[/latex]= 2512 ohm.

(a). Calculate the magnetic coupling coefficient for a maximally flat response and corresponding bandwidth.

(b). Calculate the magnetic coupling coefficient for a 0.5 dB ripple Chebyshev-type
response and corresponding bandwidth.

(c). Plot the frequency responses with PSpice simulation.

Accepted Answer

(a). The value of the coupling coefficient can be calculated from (4.57):

[latex]\left|\sigma ight|=\frac{\omega_0}{2Q}=\omega_0 \frac{k}{2}\Rightarrow k=\frac{1}{Q}[/latex] (4.57)

[latex]k=\frac{1}{Q}=\frac{1}{20}=0.05[/latex]

According to (4.58) the bandwidth is

[latex]2\Delta \omega =2 imes \left(\sqrt{2}\left|\sigma ight| ight)=\sqrt{2}\frac{\omega_0}{Q}\Rightarrow B=2\Delta f=\sqrt{2}\frac{f_0}{Q}[/latex] (4.58)

[latex]B=\sqrt{2}\frac{f_0}{Q}=\sqrt{2}\frac{2 imes 10^9}{20}=141[/latex] MHz

(b). From (4.59)

[latex]\left(\sigma ight)_C=\frac{\omega_0}{2Q}=0.709 imes \omega_0\frac{k}{2}\Rightarrow k=\frac{1}{0.709}\frac{1}{Q}=\frac{\sqrt{2}}{Q} [/latex] (4.59)

[latex]k=\frac{\sqrt{2}}{Q}=\frac{\sqrt{2}}{20}=0.0707[/latex]

From (4.60)

[latex]2\Delta \omega =2 imes \sqrt{2} imes \omega_0\frac{k}{2}=\sqrt{2} imes \omega_0 imes \frac{1}{0.709}\frac{1}{Q}\Rightarrow B=2\Delta f=2 imes \frac{f_0}{Q}[/latex] (4.60)

[latex]B=2 imes \frac{f_0}{Q}=2 imes \frac{2 imes 10^9}{20}=200[/latex] MHz

(c). Results are given in Fig. 4.24(b) that fit the calculated values.

Question 4.6: A double-tuned amplifier has a load as shown in Fig. 4.24(a)...

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