Question 23.1: Estimate the temperature performance of the resistor-MOSFET ......
Estimate the temperature performance of the resistor-MOSFET voltage references seen in Fig. 23.3. Assume that the temperature coefficient of the resistor is 2,000 ppm/C, the long-channel process is used where KP_n =120\ \mu A/V^2, and the nominal VDD is 5 V. Use simulations to verify the answers. Also show how the reference voltages change with VDD.
For the reference made using the IMEG resistor, Fig. 23.3a, the current that flows in the circuit is
I=\frac{V D D-V_{R E F}}{10^{6}}=\frac{K P_{n}}{2}\cdot\frac{W}{L}(V_{R E F}-V_{T H N})^{2}which can be solved to determine I is around 4 μA and
V_{R E F}=V_{G S}\approx900\;m VFrom Sec. 9.1.3 the rate the threshold voltage changes with temperature is
\frac{\partial V_{T H N}}{\partial T}\approx-1\;m V/C^{\circ}\approx\frac{\partial V_{R E F}}{\partial T}The temperature coefficient of the reference voltage is
T C V_{R E F}=\frac{1}{V_{R E F}}\frac{\partial V_{R E F}}{\partial T}=\frac{-0.001}{0.9}=-1,111\ p p m/C^{\circ} (23.5)
and thus
V_{R E F}(T)=V_{R E F}\cdot(1+T C V_{R E F}(T-T_{0}))=0.9\cdot(1-0.00111(T-25))) (23.6)
where we assume that the threshold voltage was measured at 25 °C. The simulation results are seen in Fig. 23.4. Note that at higher temperatures the threshold voltage decreases and thus so does V_{REF}. Further note that a change in temperature of 25 °C corresponds to a change in the reference voltage of 31.25 mV(= 25 · 0.00125).
To estimate the temperature behavior of the circuit in Fig. 23.3b, we must first determine the value of V_{REF}. Using Eq. (23.2), we can write
V_{R E F}=V_{T H N}+\sqrt{\frac{2I_D}{\beta_1} }= V_{T H N}+\sqrt{\frac{2(VDD-V_{REF})}{R\cdot \beta_1} } (23.2)
V_{R E F}=V_{T H N}\,+\,\sqrt{\frac{2(V D D-V_{R E F})}{R\cdot{\beta_1}}}\,=0.8+{\sqrt{\frac{2(5-V_{R E F})}{10k\cdot{\frac{10}{2}}\cdot120\mu A/V^{2}}}}After a few iterations, we can determine V_{REF} \approx 1.85\ V. The temperature coefficient is calculated using Eq. (23.4)
which evaluates to TCV_{REF} = 500\ ppm/C . The simulation results are seen in Fig. 23.5. Note how, when comparing Figs. 23.4 and 23.5, one reference circuit performs well with regard to temperature (23.3b), while the other reference circuit (23.3a) performs well with regard to VDD variations.
