How To Calculate Pole Of Pmos Curent Mirror

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How To Calculate Pole Of Pmos Curent Mirror
How To Calculate Pole Of Pmos Curent Mirror
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How To Calculate the Pole of a PMOS Current Mirror

Current mirrors, crucial components in many analog integrated circuits, require careful analysis to understand their frequency response. This article focuses specifically on calculating the pole of a PMOS current mirror, a vital step in determining its bandwidth and stability. Understanding this pole is key to designing high-performance circuits.

Understanding the PMOS Current Mirror

Before diving into the pole calculation, let's briefly review the PMOS current mirror's operation. A PMOS current mirror consists of two PMOS transistors: a reference transistor (M1) and a load transistor (M2). The gate and drain of M1 are connected, establishing a known current. M2's drain current mirrors M1's current, provided that M1 and M2 are matched (identical W/L ratios and operating in saturation).

Identifying the Dominant Pole

The dominant pole in a PMOS current mirror is typically determined by the output impedance of the mirror and the capacitance at the output node. This capacitance includes parasitic capacitances associated with the transistors and the interconnect. Let's break down the calculation:

1. Output Impedance (Rout)

The output impedance of the PMOS current mirror is a crucial parameter. It's approximately given by:

Rout ≈ ro2 || (gm2 * ro2 * r01)

Where:

  • ro2: Output resistance of M2. This is approximately equal to 1/(λ*ID2), where λ is the channel-length modulation parameter and ID2 is the drain current of M2.
  • gm2: Transconductance of M2. This is approximately √(2µpCox*(W/L)2*ID2), where µp is the mobility of holes, Cox is the gate oxide capacitance per unit area, W/L is the width-to-length ratio of M2, and ID2 is the drain current of M2.
  • ro1: Output resistance of M1. Similar to ro2, this is approximately 1/(λ*ID1).

2. Output Capacitance (Cout)

The output capacitance (Cout) comprises several components:

  • Cdb2: Drain-body capacitance of M2.
  • Csb2: Source-body capacitance of M2.
  • Cparasitic: Parasitic capacitances from interconnect and surrounding circuitry.

Therefore, Cout = Cdb2 + Csb2 + Cparasitic

These capacitances can be found in transistor datasheets or through simulations.

3. Calculating the Pole (ωp)

The dominant pole (ωp) of the PMOS current mirror is determined by the output impedance and capacitance:

ωp ≈ 1 / (Rout * Cout)

This ωp is in radians per second. To convert to Hertz (frequency, fp), use the following formula:

fp = ωp / (2π)

Improving Accuracy and Considerations

The above calculations provide a reasonable approximation. For a more precise analysis, consider the following:

  • Higher-Order Poles: While the dominant pole is usually sufficient, higher-order poles can impact the high-frequency response. More sophisticated analysis techniques, such as small-signal analysis using SPICE simulations, may be necessary.
  • Body Effect: The body effect can influence the output impedance. Including the body effect in the calculation leads to a more accurate result.
  • Mismatch: Mismatch between M1 and M2 will affect the accuracy of the current mirroring and, consequently, the pole frequency.

Conclusion

Calculating the pole frequency of a PMOS current mirror is essential for understanding its frequency response. The method outlined above provides a practical approach for approximating the dominant pole. However, for high-precision applications, advanced techniques like SPICE simulations are strongly recommended to account for higher-order effects and device mismatches. By accurately determining this pole, designers can ensure the stability and proper functioning of their integrated circuits.

How To Calculate Pole Of Pmos Curent Mirror
How To Calculate Pole Of Pmos Curent Mirror

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