Design the Gm – C circuit of Fig. 17.37(b) to realize a bandpass filter with a center frequency of 10 MHz, a 3-dB bandwidth of 1 MHz, and a center-frequency gain of 10. Use equal capacitors of 5 pF.

Question

Design the G_m– C circuit of Fig. 17.37(b) to realize a bandpass filter with a center frequency of 10 MHz, a 3-dB bandwidth of 1 MHz, and a center-frequency gain of 10. Use equal capacitors of 5 pF.

Accepted Answer

Using the equal-integrator-time-constants design, Eq. (17.99) yields

[latex]\frac{G_{m}}{C} = ω_{0}[/latex] (17.99)

G_m = ω₀C = 2π × 10 × 10⁶ × 5 × 10⁻¹² = 0.314 mA/V

Thus,

G_m1= G_m2 = 0.314 mA/V

To obtain G_m3, we first note that Q = f₀/BW = 10/1 = 10, and then use Eq. (17.100) to obtain

[latex]G_{m3} = \frac{G_{m}}{Q}[/latex] (17.100)

[latex]G_{m3} = \frac{G_{m}}{Q} = \frac{0.314}{10} = 0.0314 mA/V[/latex]

or

G_m3 = 31.4 μA/V

Finally, G_m4 can be found by using Eq. (17.101) as

For the BP: [latex]G_{m4} = \frac{G_{m}}{Q} |Gain| [/latex] (17.101)

[latex]G_{m4} = \frac{G_{m}}{10} × 10 = 0.314 mA/V[/latex]

Question 17.4: Design the Gm – C circuit of Fig. 17.37(b) to realize a band...

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