The model of Figure 3-1(b) can be used to verify and expand upon the previous observations. Key to understanding this model is the interaction between R_X and L as the slope compensation, m is changed. In most cases, the dependent source between R_X and C can be ignored.

If R_X is much greater than L, as is the case for little or no compensation (m = 0), the converter has a single pole response and acts as a true current mode converter. If R_X is small compared to L $m\gg \left(\frac{R_s\times V_0}{2L}\right)$ , then a double pole response is formed by the L-R-C output filter similar to any voltage-mode converter. By appropriately adjusting m, any condition between these two extremes can be generated.

Of particular interest is the case when m = $\left(\frac{R_s\times V_0}{2L}\right)$ . Since the down slope of the inductor current (m2 from Figure 2-5) is equal to (R_S V₀)/L the equation m = -½ m₂ can be derived. At this point, R_X goes to infinity, resulting in an ideal current mode converter. This is the same point, discussed in Peak Current Sensing vs. Average Current Sensing section , where the average inductor current exactly follows the error voltage. Note that although this compensation is ideal for line rejection and loop response, maximum error amplifier gain limitations as higher duty cycles are approached (see the Subharmonic Oscillation section) may necessitate using more compensation.

Having derived an equivalent circuit model, its application to more specific design examples can be discussed. Figure 3-2 plots open loop ripple rejection (ΔV₀/ΔV_I) at 120 Hz versus slope compensation for a typical 12-V buck regulator operating under the following conditions:

• V₀ = 12 V
• V_I= 25 V
• L = 200 μH
• C = 300 μF
• T = 20 μs
• R = 0.5 Ω
• R_L = 1Ω, 12Ω

$m_2=\left(\frac{V_0}{L}\right)R_s$

Again, as the slope compensation approaches m = -½ m₂, the theoretical ripple rejection is seen to become infinite. As larger values of m are introduced ripple rejection slowly degrades to that of a voltage-mode converter (-6.4 dB for this example).

If a small ripple to DC current ratio is used, as is the case for R_L = 1 Ω in the example, proportionally larger values of slope compensation UC1846 may be injected while still maintaining a high ripple rejection ratio. In other words, to obtain a given ripple rejection ratio, the allowable slope compensation may be injected while maintaining a high ripple-rejection ratio, the allowable slope compensation varies proportionally to the average DC current, not the ripple current. This is an important concept when attempting to minimize noise jitter on a low ripple converter.

Figure 3-3 shows the small signal loop response (ΔV₀/ΔVe) versus frequency for the same example of Figure 3-2. The gains have all been normalized to 0 dB at low frequency to reflect the actual difference in frequency response as slope compensation m is varied. At , m = -½ m₂ an ideal single-pole roll-off at 6 dB/octave is obtained. As higher ratios are used. the response approaches that of a double-pole with a 12-dB/octave roll-off and associated 180° phase shift.