ELEC0009: Analog Electronics

1.

The amplifier circuit shown in Figure 1.1 consists of two single stage common source amplifiers separated from each other by 𝐶2. Consider µ𝑛𝐶𝑜𝑥 = 150 µA ∙ V −2 , 𝑉𝑇𝐻 = 0.5 V and 𝑟𝑜 = ∞ for 𝑀1 and µ𝑝𝐶𝑜𝑥 = 50 µA ∙ V −2 , 𝑉𝑇𝐻 = −0.5 V and 𝑟𝑜 = ∞ for 𝑀2 . You may ignore all other second order effects and assume reasonable values for any other parameters required. Select appropriate values for the passive components in Figure 1.1 (𝑅1, 𝑅2, 𝑅3, 𝑅4, 𝑅𝐷1, 𝑅𝐷2, 𝑅𝑆1 𝑅𝑆2, 𝐶1, 𝐶2, 𝐶3), and appropriate value for ( 𝑊 𝐿 ) ratio associated with each MOSFET, where 𝑊 is the width of the transistor and 𝐿 is the channel length, to ensure that transistors are biased in saturation region and |𝐴𝑀| > 5, where 𝐴𝑀 is the mid-band value of the overall small signal gain of the circuit (𝑣𝑜𝑢𝑡 𝑣𝑖𝑛 ). Justify your selected values for all design parameters and demonstrate that all design criteria are met. [15 marks]

2.

Consider the BJT circuit shown in Figure 2.1 where 𝑅𝑠𝑖𝑔 = 10 kΩ, 𝑅𝐵 = 50 kΩ, 𝑅𝐶 = 5 kΩ, 𝑉𝐶𝐶 = 5 V , 𝑉𝐸𝐸 = −5 V , 𝐶1 = 𝐶2 = 𝐶3 = 1 µF , 𝐼𝐵𝐼𝐴𝑆 = 1 mA and for 𝑄1 , 𝑉𝐵𝐸 = 0.65 V , 𝑉𝐴 = 80 V, 𝛽 = 150, 𝐶µ = 2 pF and 𝐶𝜋 = 3 pF and 𝑟𝑥 = 20 Ω. 𝐴 is a secondary gain stage whose input impedance (𝑍𝑖𝑛) is formed of a parallel combination of an input resistance (𝑅𝑖𝑛) and an input capacitance (𝐶𝑖𝑛) where 𝑅𝑖𝑛 = 10 𝑘Ω and 𝐶𝑖𝑛 = 5 pF. The transfer function of 𝐴 (i.e. 𝐴(𝑠)) is shown below where the voltage across 𝑍𝑖𝑛 is multiplied by 𝐴(𝑠) to find 𝑣𝑜𝑢𝑡. Assume operation at room temperature.

(a) Find the mid-band magnitude[7 marks]

(b) Using appropriate methods,

(i) find all low frequency break frequencies associated with the circuit, [4 marks]

(ii) find all high frequency break frequencies associated with the circuit, [5 marks] (iii) plot the overall magnitude Bode plot of 𝑣𝑜𝑢𝑡 𝑣𝑠𝑖𝑔 within the appropriate frequency range while clearly indicating break frequencies and slopes. [4 marks]

(iii) plot the overall magnitude Bode plot within the appropriate frequency range while clearly indicating break frequencies and slopes. [4 marks]

3.

Consider the ideal series-shunt feedback circuit shown in Figure 3.1 in which amplifier 𝐴 may be characterised

(a) Select appropriate values for the resistors 𝑅1, 𝑅2, 𝑅3 and 𝑅4 to set β≈0.0005. [6 marks]

(b) Derive the expression for the gain of the feedback circuitas a function of 𝑠 for β=0.0005. [3 marks]

(c) Compare the mid-band gain-bandwidth product of the feedback circuit for β=0.0005 with that of 𝐴 in open-loop setting. [6 marks]

4.

Consider the circuit in Figure 4.1. The parameters are 𝑉+= 12 V, 𝑉−= −12 V, 𝑅𝐿 = 100 Ω, and 𝐼Bias = 5 mA. The transistor and diode parameters are 𝐼𝑆 = 10−13A. The transistor current gains are 𝛽𝑛 = 100 and 𝛽𝑝 = 20 for the npn and pnp devices, respectively.

(a) For 𝑣𝑂 = 0, determine voltage 𝑉𝐵𝐵 and the quiescent collector current and base–emitter voltage for each transistor. [8 marks]

(b) For 𝑣𝑂 = 10 V, determine the power delivered to the load and the power dissipated in each transistor. [8 marks]

5.

Consider the bipolar junction transistor op-amp circuit in Figure 5.1. The transistor parameters are: 𝛽(npn) = 110, 𝛽(pnp) = 70, 𝑉𝐴 = 90 V (all transistors), and the base-emitter turn-on voltage 𝑉𝐵𝐸(on) = 0.65 V (all transistors). The circuit parameters are: 𝑉+= 9 V, 𝑉−= −9 V, 𝐼𝑄1 = 30 μA, 𝐼𝑄2 = 250 μA, 𝑅1 = 25 kΩ, 𝐶𝐹 = 15 pF.

(a) Determine the small-signal differential-mode voltage gain. [8 marks]

(b) Find the differential-mode input resistance. [4 marks]

(c) Determine the unity-gain bandwidth. [5 marks]

6.

Figure 6.1 shows an LC-type oscillator with a bipolar junction transistor 𝑄1. Assume 𝑟𝜋 and 𝑟𝑜 of the transistor are both very large and capacitor C is tending to infinity. 𝑅𝐿 is the load and 𝐼 is an ideal current source.

(a) Derive the expression for the frequency of oscillation. [7 marks]

(b) Derive the condition of oscillation. [4 marks]

(c) If 𝑅𝐿 = 2 kΩ, 𝐼 = 2 mA , 𝑉+= 5 V and 𝑉−= −5 V, design the circuit to oscillate at 10 MHz and verify that it will sustain oscillations. [6 marks]