A three-stage staggered tuned amplifier will be designed with a center frequency of 2 GHz, having a voltage gain of 40 dB and a Chebyshev-type frequency characteristic with 0.5 dB ripple and 380 MHz bandwidth. The design will be made for a technology similar to the 0.35 micron AMS technology, but

Question

A three-stage staggered tuned amplifier will be designed with a center frequency of 2 GHz, having a voltage gain of 40 dB and a Chebyshev-type frequency characteristic with 0.5 dB ripple and 380 MHz bandwidth. The design will be made for a technology similar to the 0.35 micron AMS technology, but with an additional thick metal layer, allowing 10 nH inductors with a quality factor of 10 at 2 GHz. The Q values can be further increased with a Q-enhancement circuit similar to the circuit given in Example 4.1.

Accepted Answer

From Fig. 4.20(b) we see that the bandwidth of the circuit is [latex]B = 2\Delta \omega = 2\left|(\sigma_2)_B ight|[/latex],where[latex](\sigma_2)_B[/latex]
is the negative real center pole of a Butterworth-type circuit having the same center frequency and bandwidth. The center (real) Chebyshev pole can be calculated from (Fig. 4.18b) and Table 4.1:

r(dB)	n=2	n=3	n=4
0.05	0.898	0.75	0.623
0.1	0.859	0.696	0.567
0.2	0.806	0.631	0.505
0.3	0.767	0.588	0.467
0.4	0.736	0.556	0.439
0.5	0..709	0.524	0.416

[latex]B = 2\Delta \omega = 2\left|(\sigma_2)_B ight| [/latex]

On the other hand,

[latex]\left|(\sigma_2)_C ight| =0.524\left|(\sigma_2)_B ight|=0.524 imes \Delta \omega[/latex]

Now Q2 can be calculated as

[latex]Q_2=\frac{\omega_0}{2\Delta \omega}\frac{1}{0.524}=\frac{f_0}{2\Delta f}\frac{1}{0.524}=10.04\cong 10[/latex]

This means that the center pole can be realized without any Q-enhancement.
From Fig. 4.18(b) and Fig. 4.20(b) the tuning frequency and the quality factor corresponding to ([latex]s_{p1}[/latex])C can be calculated as

[latex]f_1=f_0-\Delta f imes \cos{(\pi/6)}=2000-190 imes 0.866=1835.46[/latex][MHz]

[latex]Q_1=\frac{\omega_1}{\left|2(\sigma_1)_C ight| },(\sigma_1)_C=0.524(\sigma_1)_B,(\sigma_1)_B=\Delta \omega imes \sin{(\pi/6)}[/latex]

[latex]Q_1=18.4[/latex]

which correspond to a resonance impedance (effective parallel resistance) of

[latex]R_{1(eff)}=L_1\omega_1 Q_1=(10 imes 10^{-9}) imes (2\pi imes 1835.46 imes 10^6) imes 18.35=2121 \Omega[/latex]

Similarly, the tuning frequency, the quality factor and the effective parallel
resistance corresponding to (sp3)C can be found as
[latex]f_3 = 2164.5 MHz, Q_3 = 21.7 R_{3(eff)} = 2949[/latex] ohm

Since the resonance circuit tuned to 2000 MHz was intended to be used without any Q-enhancement, its quality factor and the effective parallel resistance are Q = 10 and [latex]R_{2(eff)} = 1256[/latex] ohm, respectively.

The basic circuit diagram is given in Fig. 4.21(a).

As the individual stages of this amplifier, the cascode configuration is the natural choice, as explained in 4.2.2.

The tuning frequencies of these stages will be [latex]f_1, f_2 = f_0[/latex] and [latex]f_3[/latex].

To obtain the targeted voltage gain of 100 at the center frequency ([latex]f_0 = f_2[/latex]), as well as frequencies corresponding to [latex](s_{p1})_C[/latex] and [latex](s_{p3})_C[/latex], the gains of the individual stages must be properly determined.

Question 4.5: A three-stage staggered tuned amplifier will be designed wit...

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