Question 4.5: A three-stage staggered tuned amplifier will be designed wit...
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.
From Fig. 4.20(b) we see that the bandwidth of the circuit is B = 2\Delta \omega = 2\left|(\sigma_2)_B\right|,where(\sigma_2)_B
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 |
On the other hand,
\left|(\sigma_2)_C\right| =0.524\left|(\sigma_2)_B\right|=0.524\times \Delta \omegaNow Q2 can be calculated as
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 10This 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 (s_{p1})C can be calculated as
f_1=f_0-\Delta f\times \cos{(\pi/6)}=2000-190\times 0.866=1835.46[MHz]
Q_1=\frac{\omega_1}{\left|2(\sigma_1)_C\right| },(\sigma_1)_C=0.524(\sigma_1)_B,(\sigma_1)_B=\Delta \omega \times \sin{(\pi/6)}Q_1=18.4
which correspond to a resonance impedance (effective parallel resistance) of
R_{1(eff)}=L_1\omega_1 Q_1=(10\times 10^{-9})\times (2\pi \times 1835.46\times 10^6)\times 18.35=2121 \OmegaSimilarly, the tuning frequency, the quality factor and the effective parallel
resistance corresponding to (sp3)C can be found as
f_3 = 2164.5 MHz, Q_3 = 21.7 R_{3(eff)} = 2949 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 R_{2(eff)} = 1256 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 f_1, f_2 = f_0 and f_3.
To obtain the targeted voltage gain of 100 at the center frequency (f_0 = f_2), as well as frequencies corresponding to (s_{p1})_C and (s_{p3})_C, the gains of the individual stages must be properly determined.
